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Advanced Classical Mechanics/Central Forces

Central forces are forces between two particles that depend only on the distance between the particles and point from one particle to another. Central forces are conservative (why?). Furthermore, if we look at a central force between two particles we can separate the motion of the center of mass from the relative motion of the particles reducing the complexity of the problem.

Separation of Motion
We have two particles of masses $$m_1$$ and $$m_2$$ located at positions $$\vec r_1$$ and $$\vec r_2$$. Furthermore, let's define $$\vec r=\vec r_1 - \vec r_2$$. Let's assume that the potential depends only on the relative position of the two particles. We can write out the Lagrangian as

$$ L = T - V = \frac{1}{2} m_1 \dot \vec r_1^2 + \frac{1}{2} m_2 \dot \vec r_2^2 - V \left ( \vec r \right ) + m_1 \vec g \cdot \vec r_1 + m_2 \vec g \cdot \vec r_2 $$

where $$\vec g$$ is the direction of the acceleration due to a uniform gravitational field.

Let's define $$\vec R$$ to be the position of the center of mass

$$ \vec R=\frac{m_1 \vec r_1 + m_2 \vec r_2}{m_1+m_2} $$

so

$$ \vec r_1 = \vec R + \frac{m_2 \vec r}{m_1 + m_2} $$ and $$ \vec r_2 = \vec R - \frac{m_1 \vec r}{m_1 + m_2}. $$

Lagrangian
Let's write out the Lagrangian using the new coordinates

$$ L = \frac{1}{2} m_1 \left ( \dot \vec R^2 + 2 \dot \vec R \cdot \dot \vec r \frac{m_2}{m_1+m_2} + \dot \vec r^2 \frac{m_2^2}{\left (m_1+m_2\right )^2} \right ) + $$

$$ \frac{1}{2} m_2 \left ( \dot \vec R^2 - 2 \dot \vec R \cdot \dot \vec r \frac{m_1}{m_1+m_2} + \dot \vec r^2 \frac{m_1^2}{\left (m_1+m_2\right )^2} \right ) - $$

$$ V \left (\vec r \right ) + m_1 \vec g \cdot \left ( \vec R + \frac{m_2 \vec r}{m_1 + m_2} \right ) + m_2 \vec g \cdot \left ( \vec R - \frac{m_1 \vec r}{m_1 + m_2} \right ) $$

Notice that the middle terms in the first two sets of parentheses and the final terms in the final set cancel each other out and we are left with

$$ L = \frac{1}{2} M \dot \vec R^2 + \frac{1}{2} \mu \dot \vec r^2 - V \left (\vec r \right ) + M \vec g \cdot \vec R $$

where $$M=m_1+m_2$$ is the total mass and the reduced mass is $$ \mu = \frac{m_1 m_2}{m_1 + m_2} $$

So we find that for two bodies the dynamics reduces to the motion of the center of mass (possibly in a uniform gravitational field) and the motion of single particle about the center of mass.

Angular Momentum
Let's calculate the total angular momentum of the system. We know from the results on many-particle systems that the angular momentum of the system will separate into the angular momentum about the center of mass and that of the center of mass. Furthermore, if $$V\left ( \vec r \right ) = V \left ( \left | \vec r \right | \right )$$, the internal forces do not contribute to the change in the angular momentum. We have

$$ \vec L = m_1 \vec r_1 \times \vec v_1 + m_2 \vec r_2 \times v_2 $$

$$ = m_1 \left ( \vec R + \frac{m_2 \vec r}{m_1 + m_2} \right ) \times \left ( \vec V + \frac{m_2 \vec v}{m_1 + m_2}\right ) + m_2 \left (  \vec R - \frac{m_1 \vec r}{m_1 + m_2} \right ) \times \left ( \vec V - \frac{m_1 \vec v}{m_1 + m_2}\right ) $$

where $$\vec v=\vec v_1 - \vec v_2$$ and $$\vec V = \left ( m_1 \vec v_1 + m_2 \vec v_2 \right ) / M$$.

$$ \vec L = M \vec R \times \vec V + \left [ m_1 \frac{m_2^2}{\left ( m_1 + m_2 \right )^2} + m_2 \frac{m_1^2}{\left ( m_1 + m_2 \right)^2} \right ] \left ( \vec r \times \vec v \right ) = M \vec R \times \vec V + \mu \vec r \times \vec v. $$

We know from the results on many-particle systems in a uniform gravitational field that the internal angular momentum ($$\mu \vec r \times \vec v$$) of the two-body system is conserved. We could have seen this from separation of the internal and external degrees of freedom in the Lagrangian.

General Results
We can treat the central force between two particles as a force between a fixed center that we take to be the origin and a single particle. We have

$$ L = \frac{1}{2} \mu \dot \vec r^2 - V \left (\left | \vec r \right |\right ), $$

Taking the particular case of the results from the first section where the potential does not depend on direction, we know that the angular momentum of the particle is conserved. This means that the motion will be restricted to a plane that we will take to be the equatorial plane ($$\theta=\pi/2$$) without a loss of generality. Let's write the Lagrangian in spherical coordinates. First let's write the position of the particle in terms of the spherical coordinates. We have

$$ \vec r = \left [ \begin{matrix} r \sin \theta \cos \phi \\ r \sin \theta \sin \phi \\ r \cos \theta \end{matrix} \right ] $$

and

$$ \dot \vec r = \left [ \begin{matrix} \dot r \sin \theta \cos \phi + r \dot \theta \cos \theta \cos \phi - r \dot \phi \sin \theta \sin \phi \\ \dot r \sin \theta \sin \phi + r \dot \theta \cos \theta \sin \phi + r \dot \phi \sin \theta \cos \phi \\ \dot r \cos \theta - r \dot \theta \sin \theta \end{matrix} \right ] $$

so

$$ \dot \vec r^2 = \dot r^2 + r^2 \dot \theta^2 + r^2 \dot \phi^2 \sin^2\theta. $$

Lagrangian
Let's write out the Lagrangian in terms of the spherical coordinates

$$ L = \frac{1}{2} \mu \left ( \dot r^2 + r^2 \dot \theta^2 + r^2 \dot \phi^2 \sin^2\theta\right ) - V(r). $$

Conserved Quantities
First let's notice that $$\partial L/\partial \phi = 0$$ so $$p_\phi$$ is conserved. Also $$\partial L/\partial t=0$$ so $$H$$ is conserved as well.

Let's calculate the conserved momentum,

$$ p_\phi = \frac{\partial L}{\partial \dot \phi} = \mu r^2 \dot \phi\sin^2 \theta $$

which has units of angular momentum. It is simply the angular momentum about the $$z-$$axis.

Equations of Motion
We can also use Lagrange's equation to get the equations of motion

$$ \frac{d}{dt} \frac{\partial L}{\partial \dot \theta} - \frac{\partial L}{\partial \theta} = 0, $$

$$ \frac{d}{dt} \left ( \mu r^2 \dot \theta \right ) = 2 \mu r \dot r \dot \theta + \mu r^2 \ddot \theta = \mu r^2 \dot \phi^2 \sin \theta \cos \theta. $$

If $$\dot \theta=0$$ and $$\theta=0,\pi/2$$ or $$\pi$$ initial, then $$\ddot \theta=0$$ and $$\theta$$ stays constant. We take $$\theta=\pi/2$$ and $$\dot \theta=0$$ initially, so the particle remains in the equatorial plane as we expected from the conservation of angular momentum.

Now for the radial motion,

$$ \frac{d}{dt} \frac{\partial L}{\partial \dot r} - \frac{\partial L}{\partial r} = 0, $$

$$ \frac{d}{dt} \left ( \mu \dot r \right ) - r \mu \dot \theta^2 - r \mu \dot \phi^2 \sin^2 \theta + \frac{\partial V}{\partial r} = 0. $$

Using the initial conditions we have

$$ \ddot r = -\frac{1}{\mu} \frac{\partial V}{\partial r} + r \dot \phi^2 = -\frac{1}{\mu} \frac{\partial V}{\partial r} + \frac{p_\phi^2}{\mu^2} \frac{1}{r^3}. $$

where the dependence of the acceleration on the angle $$\phi$$ has been included through the conserved quantity $$p_\phi$$, separating the radial equation from the angular equation. The first term is the force between the two bodies and the second term is a 'fictitous' force because of the spherical coordinates. We will solve this differential equation for two special cases, but we can get a good idea of the nature of the motion by looking at the conserved quantities.

Bounded Motion
First, we have

$$ p_\phi = \mu r^2 \dot \phi = \mu dA/dt $$

so the path subtends equal areas in equal times. Given a solution for the radial motion we can determine the angular motion

$$ \dot \phi = \frac{p_\phi}{\mu} \frac{1}{r^2}. $$

Second we have the Hamiltonian,

$$ H = \dot r \frac{\partial L}{\partial \dot r} + \dot \theta \frac{\partial L}{\partial \dot \theta} + \dot \phi \frac{\partial L}{\partial \dot \phi} - L = \frac{1}{2} \mu \left ( \dot r^2 + r^2 \dot \theta^2 + r^2 \dot \phi^2 \sin^2\theta\right ) + V(r) $$

Because the Hamiltonian is conserved, let's take its initial value to be

$$ E = \frac{1}{2} \mu \dot r^2 + \frac{1}{2} \frac{p_\phi^2}{\mu} \frac{1}{r^2} + V(r). $$

We can solve this for $$\dot r^2$$ to get

$$ \dot r^2 = \frac{2 E}{\mu} - \frac{p_\phi^2}{\mu^2} \frac{1}{r^2} - \frac{2 V(r)}{\mu} $$

which is very similar to the one-dimensional case but with an added term for the centrifugal force. Unless $$V \sim r^n$$ as $$r\rightarrow 0$$ with $$n\leq -2$$ and $$V$$ is negative, motion of the the particle is bounded if $$p_\phi \neq 0$$. This point of closest approach is called the pericenter. Depending on the potential and the initial conditions, the motion may be bounded at large $$r$$ as well. In particular if the potential is attractive and positive there is always a point of maximum distance. The point of maximum radius is called the apocenter.

If the motion is bounded at both large and small radius, we can calculate the time for the particle to go from the minimum to maximum radius -- this is one half of the period of the complete radial motion as we did for the one-dimensional pendulum. The angular motion as we shall find can have a different (and not usually comeasureable) period. We have

$$ \frac{d r}{d t} = \sqrt { \frac{2 E}{\mu} - \frac{p_\phi^2}{\mu^2} \frac{1}{r^2} - \frac{2V(r)}{\mu} } $$

and rearranging we have

$$ P = 2 \int_{r_{\rm min}}^{r_{\rm max}} \frac{dr}{ \sqrt { \frac{2 E}{\mu} - \frac{p_\phi^2}{\mu^2} \frac{1}{r^2} - \frac{2 V(r)}{\mu} } } $$

Central Force Solution
For a spherical harmonic oscillator, $$ V = k r^2/2. $$

Bounds of Motion
Let's first calculate the bounds of the motion we have

$$ 0 = \frac{2 E}{\mu} - \frac{p_\phi^2}{\mu^2} \frac{1}{r^2} - \frac{k r^2}{\mu} $$

which yields a quadratic equation for $$r^2$$,

$$ r^4 - \frac{2 E}{k} r^2 + \frac{p_\phi^2}{\mu k} = 0 $$

which yields the solutions

$$ r_{\pm}^2 = \frac{E}{k} \pm \sqrt{\frac{E^2}{k^2} - \frac{p_\phi^2}{\mu k}} $$

Radial Motion
We will first use the conservation of energy to calculate the radial motion, we have

$$ t_1 - t_0 = \int_{r_0}^{r_1} \frac{dr}{\sqrt{\frac{2E}{\mu}-\frac{k}{\mu} r^2 - \frac{p_\phi^2}{r^2 \mu^2} }} = \sqrt{\frac{\mu}{k}} \int_{r_0}^{r_1} \frac{r dr}{\sqrt{\left (r_+^2-r^2\right )\left (r^2-r_-^2\right ) }} $$

$$ = \frac{1}{2} \sqrt{\frac{\mu}{k}} \int_{r_0^2}^{r_1^2} \frac{d \left ( r^2 \right )}{\sqrt{\left (r_+^2-r^2\right )\left (r^2-r_-^2\right ) }}. $$

To perform this integral let's make the substitution

$$ s=\frac{2 r^2 - \left (r_+^2 + r_-^2 \right )}{r_+^2 - r_-^2} $$

to give

$$ t_1 - t_0 = \frac{1}{2} \sqrt{\frac{\mu}{k}} \int_{r=r_0}^{r=r_1} \frac{d s}{\sqrt{1-s^2}} = \left. \frac{1}{2} \sqrt{\frac{\mu}{k}} \arcsin s \right |_{r=r_0}^{r=r_1} $$

so

$$ r^2 = \frac{r_+^2 + r_-^2}{2} + \frac{r_+^2-r_-^2}{2} \sin \left [ 2 \sqrt{\frac{k}{\mu}} \left ( t - t_0 \right ) + \psi_0 \right ] $$

$$ = \frac{E}{k} + \sqrt{\frac{E^2}{k^2} - \frac{p_\phi^2}{\mu k}} \sin \left [ 2 \sqrt{\frac{k}{\mu}} \left ( t - t_0 \right ) + \psi_0 \right ] $$

with

$$ \psi_0 = \arcsin \left [ \frac{2 r_0^2 - \left (r_+^2 + r_-^2 \right )}{r_+^2 - r_-^2} \right ] = \arcsin \left [ \frac{r_0^2 - \frac{E}{k}}{\sqrt{\frac{E^2}{k^2} - \frac{p_\phi^2}{\mu k}}} \right ] $$

Angular Motion
What remains is to solve for the motion in the $$\phi-$$direction. Using the conservation of angular momentum we have

$$ \frac{\partial \phi}{\partial t} = \frac{p_\phi}{\mu} \frac{1}{r^2} = \frac{p_\phi}{\mu} \frac{1}{\frac{r_+^2 + r_-^2}{2} + \frac{r_+^2-r_-^2}{2} \sin \left [ 2 \sqrt{\frac{k}{\mu}} \left ( t - t_0 \right ) + \psi_0 \right ]}. $$

We can integrate this directly to yield

$$ \phi = \frac{p_\phi}{\sqrt{k\mu} r_+ r_-} \arctan \left \{ \frac{1}{2 r_+ r_-} \left [ \left (r_+^2 + r_-^2 \right ) \tan \left ( \sqrt{\frac{k}{\mu}} \left ( t-t_0 \right ) + \psi_0 \right ) + r_+^2 -r_-^2 \right ] \right \}. $$

Notice that the angular frequency is $$\sqrt{k/m}$$, one-half of the radial frequency.

If we substitute the values of $$r_+$$ and $$r_-$$ we get

$$ \phi = \arctan \left \{ \sqrt{\frac{\mu E^2}{p_\phi^2 k}} \left [  \tan \left ( \sqrt{\frac{k}{\mu}} \left ( t-t_0 \right ) + \psi_0 \right ) + \sqrt{ 1 - \frac{p_\phi^2 k}{\mu E^2}} \right ] \right \}. $$

It is possible to write $$r$$ as a function of $$\phi$$ and find that it is the equation for an ellipse centered at the origin. This is left as an exercise for the reader.

The Shape of the Orbit
Let's step back and try to determine $$r(\phi)$$ instead of $$r(t)$$. First we define $$u=1/r^2$$ so we have

$$ \frac{du}{d\phi} = -\frac{2}{r^3} \frac{dr}{d\phi} $$

and using the chain rule we get

$$ \dot r = \frac{dr}{d\phi} \dot \phi = -\frac{r^3}{2} \dot \phi \frac{du}{d\phi} = - \frac{r}{2} \frac{p_\phi}{\mu} \frac{du}{d\phi}. $$

We can substitute this into the energy equation to get

$$ \dot r^2 = \frac{r^2}{4} \frac{p_\phi^2}{\mu^2} \left ( \frac{du}{d\phi} \right )^2 = \frac{1}{4 u} \frac{p_\phi^2}{\mu^2} \left ( \frac{du}{d\phi} \right )^2 =\frac{2 E}{\mu} - \frac{p_\phi^2}{\mu^2} u - \frac{k}{\mu u} $$

and rearranging

$$ \left ( \frac{du}{d\phi} \right )^2 + 4 u^2 - \frac{8 E \mu}{p_\phi^2} u = -\frac{4 k \mu}{p_\phi^2}. $$

We add a constant to both sides of the equation to complete the square

$$ \left [ \frac{d}{d\phi} \left ( u - \frac{E \mu}{p_\phi^2} \right ) \right ]^2 + 4 \left ( u - \frac{ E \mu}{p_\phi^2} \right )^2  = -\frac{4 k \mu}{p_\phi^2} + 4 \left ( \frac{E \mu}{p_\phi^2} \right )^2 $$

We find that the derivative of a function squared plus four times the function itself yields a constant, so the function must be a sine or cosine. We have $$ u - \frac{E \mu}{p_\phi^2} = \left [ \left ( \frac{E \mu}{p_\phi^2} \right )^2  - \frac{ k \mu}{p_\phi^2} \right ]^{1/2} \cos  2 \left  ( \phi - \phi_0 \right ). $$

We can write this in terms of the radius

$$ r^2 =\frac{p_\phi^2}{E\mu} \frac{1}{ \left ( 1 - \frac{k p_\phi^2}{E^2 \mu} \right )^{1/2} \cos  2 \left  ( \phi - \phi_0 \right ) + 1}. $$

This is the equation for an ellipse centered on the origin. The constant in front of the cosine is related to the shape of the ellipse

$$ \left ( 1 - \frac{k p_\phi^2}{E^2 \mu} \right )^{1/2} = \frac{e^2}{2-e^2} $$

where $$e^2=1-b^2/a^2$$ is the square of the eccentricity of the ellipse ($$a$$ and $$b$$ are the semimajor and semiminor axes). If and only if the spring constant is negative (repulsive spring), then the eccentricity can be greater than one (up to $$\sqrt{2}$$ and the curve is a hyperbola centered on the origin. An interesting case is $$k=0$$ so $$e=1$$.  This gives a straight line passing a distance $$p_\phi/\sqrt(2E\mu)$$ from the origin.

Cartesian Solution
We can solve the spherical harmonic oscillator in Cartesian coordinates as well. We have for the Lagrangian

$$ L = \frac{1}{2} \mu \left ( \dot x^2 + \dot y^2 + \dot z^2 \right ) - \frac{1}{2} k \left ( x^2 + y^2 + z^2 \right ) $$

which yields the following equation of motion for the $$x-$$coordinate

$$ \mu \ddot x + k x = 0 $$

and similarly for the other directions. We find the following solution for the motion in the $$x-$$direction

$$ x(t) = A \cos \left ( \omega t + a \right ) $$

with $$\omega^2=k/\mu$$ and similarly for the other coordinates. Since the value of $$\omega$$ is the same for all three directions we find that the figure is an ellipse. We can also calculate the value of $$r^2$$

$$ r^2 = A^2 \cos^2 \left ( \omega t + a \right ) + B^2 \cos^2 \left ( \omega t + b \right ) $$

where for simplicity and without loss of generality we have restricted the motion to the $$x-y-$$plane. We have

$$ r^2 = \frac{A^2}{2} \left [ 1 + \cos \left (2 \omega t + a \right ) \right ] + \frac{B^2}{2} \left [ 1 + \cos \left (2 \omega t + b \right ) \right ] $$

$$ = \frac{A^2+B^2}{2} + \frac{A^2}{2} \cos \left (2 \omega t + a \right ) + \frac{B^2}{2} \cos \left (2 \omega t + b \right ) $$

We can rewrite these two cosines as a single cosine,

$$ r^2 = \frac{A^2+B^2}{2} + \frac{1}{2} \sqrt{ A^4 + B^2 + 2 A^2 B^2 \cos \left (a - b\right ) } \cos \left [ 2\omega t + \psi_0 \right ] $$

where

$$ \psi_0 = \arccos \frac{A^2 \cos a + B^2 \cos b}{\sqrt{ A^4 + B^2 + 2 A^2 B^2 \cos \left (a - b\right ) }} $$

which has the same form as the result for the spherical analysis.

Gravity
For gravity we have

$$ V = - \frac{G m_1 m_2}{r} = - \frac{G \mu M}{r} = $$

yielding the following Lagrangian,

$$ L = \frac{1}{2} \mu \left ( \dot r^2 + r^2 \dot \theta^2 + r^2 \dot \phi^2 \sin^2\theta\right ) + \frac{G \mu M}{r}. $$

Bounds of the Motion
Let's first calculate the bounds of the motion we have

$$ 0 = \frac{2 E}{\mu} - \frac{p_\phi^2}{\mu^2} \frac{1}{r^2} + \frac{2 G M}{r} $$

which yields a quadratic equation for $$r$$

$$ r^2 + \frac{G M \mu}{E} r - \frac{p_\phi^2}{E \mu} = 0 $$

which yields the solutions

$$ r_{\pm} = -\frac{G M\mu}{2 E} \pm \sqrt{ \left (\frac{G M \mu}{2 E}\right)^2 + \frac{p_\phi^2}{E \mu}}. $$

For the case of an attractive force $$G>0$$ we find that if $$E>0$$, only $$r_+$$ is greater than zero and this represents the point of closest approach. On the other hand if $$E<0$$ we have $$r_-< r < r_+$$. For a repulsive force $$G<0$$ and again only $$r_+$$ is greater than zero if $$E>0$$. If both $$G$$ and $$E$$ are negative, we cannot find a positive value of $$r$$ with $$\dot r^2>0$$.

Radial Motion
We can also solve for the radial velocity

$$ \dot r^2 =\frac{2 E}{\mu} - \frac{p_\phi^2}{\mu^2} \frac{1}{r^2} + \frac{2 G M}{r} = \frac{2 E}{\mu r^2} \left ( r^2 + \frac{G M \mu}{E} r - \frac{p_\phi^2}{E \mu} \right ) = \frac{2 E}{\mu r^2} \left ( r - r_+ \right ) \left ( r - r_- \right ). $$

Yielding the following equation for the time evolution

$$ t_1 - t_0 = \sqrt {\frac{\mu}{2E} } \int_{r_0}^{r_1} \frac{r}{\sqrt{\left ( r - r_+ \right ) \left ( r - r_- \right )} }d r $$

and let's make the substitution

$$ s=\frac{2 r - \left (r_+ + r_- \right )}{r_+ - r_-} $$

to give the following integral

$$ t_1 - t_0 = \sqrt {-\frac{\mu}{2E} } \frac{r_+-r_-}{2} \int_{r=r_0}^{r=r_1} \frac{s}{\sqrt{1-s^2}} + \frac{r_+ + r_-}{\sqrt{1-s^2}} d s $$

where we have assumed that $$E<0$$. This gives

$$ t_1 - t_0 = \left. \sqrt {-\frac{\mu}{2E} } \frac{r_+-r_-}{2} \left [ \left ( r_+ + r_- \right ) \arcsin s - \sqrt{1-s^2} \right ]  \right |_{r=r_0}^{r=r_1} $$

and for $$E>0$$ we have

$$ t_1 - t_0 = \left. \sqrt {\frac{\mu}{2E} } \frac{r_+-r_-}{2} \left [ \left ( r_+ + r_- \right ) {\rm arcsinh} s - \sqrt{s^2-1} \right ]  \right |_{r=r_0}^{r=r_1} $$

Unfortunately we cannot invert this to find the radius as a function of time, but we can determine, the time to go from the minimum to the maximum radius in the $$E<0$$ case

$$ P = \pi \sqrt{-\frac{\mu}{2E}} \left ( r_+^2 - r_-^2 \right ) = \pi \sqrt{-\frac{\mu}{2E}} \frac{G M \mu}{-E} \sqrt{\left(\frac{G M \mu}{E}\right)^2 + \frac{4 p_\phi^2}{E \mu}} $$

The Shape of the Orbit
Let's step back and try to determine $$r(\phi)$$ instead of $$r(t)$$. First we define $$u=1/r$$ so we have

$$ \frac{du}{d\phi} = -\frac{1}{r^2} \frac{dr}{d\phi} $$

and using the chain rule we get

$$ \dot r = \frac{dr}{d\phi} \dot \phi = -r^2 \dot \theta \frac{du}{d\theta} = - \frac{p_\phi}{\mu} \frac{du}{d\phi}. $$

We can substitute this into the energy equation to get

$$ \dot r^2 = \frac{p_\phi^2}{\mu^2} \left ( \frac{du}{d\phi} \right )^2 = \frac{2 E}{\mu} - \frac{p_\phi^2}{\mu^2} u^2 + 2 G M u $$

and rearranging

$$ \left ( \frac{du}{d\phi} \right )^2 + u^2 - \frac{2 G M \mu^2 u}{p_\phi^2} = \frac{2E\mu}{p_\phi^2} $$

Let's define the length $$l=p_\phi^2/(G M \mu^2)$$ and simplify the equation

$$ \left ( \frac{du}{d\phi} \right )^2 + u^2 - \frac{2}{l} u = \frac{2E}{G M \mu l}. $$

Let's add $$1/l^2$$ to both sides of the equation and get

$$ \left [ \frac{d}{d\phi} \left( u - \frac{1}{l} \right ) \right ]^2 + \left ( u - \frac{1}{l} \right )^2 = \frac{2E}{G M \mu l} + \frac{1}{l^2}. $$

We have a function squared plus its first derivative squared being a constant. The function is clearly a trigonometric function we have

$$ u = \frac{1}{r} = \frac{e}{l} \cos \left ( \phi- \phi_0 \right ) + \frac{1}{l} $$

where

$$ e^2 = \frac{2E l}{G M \mu} + 1. $$

Rearranging the equation gives

$$ r \left [ e \cos \left ( \phi - \phi_0 \right ) + 1 \right ] = l $$

which is the polar equation for an ellipse with its focus at the origin for $$01$$ the curve is a hyperbola. $$e=1$$ is a parabola and $$e=0$$ is a circle. (Contrast this with the spherical harmonic oscillator where the center of the ellipse was at the origin).

If we have a repulsive force (e.g. the force between two positive charges) $$e \geq 1$$ because $$E \geq 0$$. The resulting curve is a hyperbola.

The figure shows the various conic sections as a function of the value $$e$$, the eccentricity. The blue parabola has $$e=1$$, the aqua ellipse has $$e=0.5$$ and the green circle has $$e=0$$. The red hyperbola has $$e=2$$. All of the curves have a focus at the origin and $$l=1$$. The semi-latus rectum is the official name for the quantity $$l$$ which sets the size of the curve. In all cases the curve intersects the $$y-$$axis at $$y=\pm 1$$. In a coordinate free way, the semi-latus rectum is the distance between the curve and the focus in the direction perpendicular to the point of closest approach.

What is the meaning of the two branches of the hyperbola? The left branch is for an attactrive force and the right branch is for a repulsive force.


text:
Sar Gerik

Sar Gerik (, also Romanized as Sar Gerīk and Sar Gerig) is a village in Binalud Rural District, in the Central District of Nishapur County, Razavi Khorasan Province, Iran. At the 2006 census, its population was 49, in 10 families.

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title: Sar Gerik


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Strategic Studies/Universal Operational Simulation

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text:
Urho Toivola

Urho Vilpitön Konstantin Toivola (until 1906 Kröger; 17 October 1890 – 11 September 1960) was a Finnish journalist, Member of Parliament and a diplomat. He represented left-wing liberalism, so-called Jacobinism in the National Progressive Party.

Early life
Toivola was born in Heinola. His parents were Reverend David Konstantin Kröger and Anni Koponen. He graduated from secondary school in 1909 and graduated with a Bachelor of Philosophy in 1914.

Journalist
Toivola worked as a journalist for Pohjanlahti magazine in Rauma and the Helsingin Sanomat newspaper in 1915. Toivola became Editor-in-Chief for Turun Sanomat from 1925 to 1937, in the Elanto newspaper from 1937 to 1938 and also in Le Nord magazine in 1938.

In 1930, as a member of a delegation of European journalists which also included Felix Salten, invited by the Carnegie Endowment for International Peace, he visited the United States and wrote a book on his journey, Aurinkoista Amerikkaa.

Politician
After holding positions such as party secretary in the Young Finnish Party, official in the National Food Authority and secretary both in the consumers' co-operative of Elanto and in the National Progressive Party,

In the early 1920s, Toivola served as Secretary at the Finnish Embassy in London from 1921 to 1922, and in the Finnish Embassy in Paris and as Finland's Representative at the League of Nations from 1922 to 1925 and was Secretary of the Finnish Delegation to the General Assembly in the League of Nations from 1922 to 1924.

After joining the Ministry for Foreign Affairs, Toivola was the Head of the Ministry's newspaper Department from 1938 to 1939, and Head of the Information Center in the Council of State in 1939 and Chargé d'Affaires of Finland to Oslo in 1940 and during the Continuation War as Counselor in Washington from 1941 to 1944.

After the war, Toivola served as Finnish Envoy to Ottawa from 1948 to 1952, and in Prague, and in Vienna from 1953 to 1957.

Toivola was Member of Parliament from 1933 to 1936 from the southern constituency of the Turku County. He was elector in several presidential elections in 1931, 1937 and 1940.

He was a member in the City Council of Turku and was a member of the Young Finnish Party's Central Committee and later member in the National Progressive Party's subcommittee.

Personal life
Toivola married Lyyli Elisabeth (Rakel) Kansanen from 1913 to 1949. Ambassador Joel Toivola was their son. As a widower, Urho Toivola married a second time in 1951 to Rachel Ilona Kansanen who had a Bachelor of Philosophy degree.

He died in Helsinki, aged 69.

title: Urho Toivola


text:
GCSE Science/Forces

 * How can we describe the way things move?
 * How do we make things speed up or slow down?
 * Acceleration (advanced)
 * Force
 * Balanced and Unbalanced Forces
 * F = ma (advanced)
 * Kinetic energy
 * Momentum
 * Gravity and Astronomy

title: GCSE Science/Forces


text:
Talk:David Thomas (musician)

David Thomas and two pale boys
On all official websites I see this spelling: David Thomas and two pale boys. --Pettsams 01:30, 10 August 2007 (UTC)

Punk vs Post-Punk
The page claimed Pere Ubu was post-punk rather than just punk. I changed this, because Pere Ubu was founded in 1975, two years before the term "punk" was coined. This makes the band contemporaries, not followers, of the Sex Pistols, Ramones, Devo, etc. Post-punk implies that it happened AFTER punk, when Pere Ubu was happening at the same time. --<IP_ADDRESS> (talk) 21:29, 4 February 2009 (UTC)
 * Since Ubu predated punk, they count as "proto-punk." However, the music they were doing as early as 1975 was also on the artistic level today known as "post-punk." So they were already post-punk even before there was punk! I really think that the only such term applicable to them is "proto-post-punk" (which probably makes them one of a kind). I say that only half in jest.

 * However, I like their self-designation "avant garage" the best. It's clever. Johanna-Hypatia (talk) 03:53, 8 September 2013 (UTC)

Fair use rationale for Image:DTWave.jpg
Image:DTWave.jpg is being used on this article. I notice the image page specifies that the image is being used under fair use but there is no explanation or rationale as to why its use in this Wikipedia article constitutes fair use. In addition to the boilerplate fair use template, you must also write out on the image description page a specific explanation or rationale for why using this image in each article is consistent with fair use.

BetacommandBot (talk) 06:42, 2 January 2008 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified one external link on David Thomas (musician). Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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External links modified
Hello fellow Wikipedians,

I have just modified one external link on David Thomas (musician). Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20070928000228/http://www.disinfo.com/archive/pages/article/id502/pg1/ to http://www.disinfo.com/archive/pages/article/id502/pg1/

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title: Talk:David Thomas (musician)


text:
Egon Freiherr von Eickstedt

Egon Freiherr von Eickstedt (Egon Rudolf Ernst Adolf Hans Dubslaff Freiherr von Eickstedt) (April 10, 1892 – December 20, 1965) was a German physical anthropologist who classified humanity into races. His study in the classification of human races made him one of the leading racial theorists of Nazi Germany.

Early life
Egon Freiherr von Eickstedt was born on April 10, 1892, in Jersitz, Province of Posen.

Career
Von Eickstedt was an anthropologist. He was the author of Rassenkunde und Rassengeschichte der Menschheit (Ethnology and the Race History of Mankind).

From 1935 to 1944, he was the editor of Zeitschrift für Rassenkunde, a German journal of racial studies, with co-editors including Hans F. K. Günther.

After the World War II, in 1949, Eickstedt established a journal Homo. Internationale Zeitschrift für die vergleichende Forschung am Menschen as the successor of the Zeitschrift für Rassenkunde.

Death
He died on December 20, 1965.

title: Egon Freiherr von Eickstedt


text:
Wikipedia:Articles for deletion/Jessa Duggar

The result was   keep. Nakon 02:30, 22 February 2015 (UTC)

Jessa Duggar

 * – ( View AfD View log  Stats )

Not independently notable. Possible worth a redirect to article on Duggar family. Boleyn (talk) 22:55, 8 February 2015 (UTC)
 * Redirect this and Jill Duggar to 19 Kids and Counting. Merge any content that isn't already on the latter article. —  Noah  00:12, 9 February 2015 (UTC)
 * Note: This debate has been included in the list of Arkansas-related deletion discussions. lavender|(formerlyHMSSolent)|lambast 00:13, 9 February 2015 (UTC)
 * Note: This debate has been included in the list of Actors and filmmakers-related deletion discussions. lavender|(formerlyHMSSolent)|lambast 00:13, 9 February 2015 (UTC)

 * Redirect to 19 Kids and Counting, its fine to redirect it but lacks WP:BLP Changed vote to keep it looks good and meets with guidelines below plus sources. ApprenticeFan  work 13:42, 9 February 2015 (UTC)
 * Note: This debate has been included in the list of Authors-related deletion discussions. • Gene93k (talk) 14:56, 11 February 2015 (UTC)

 Relisted to generate a more thorough discussion so a clearer consensus may be reached.
 * Keep per WP:GNG. The fact is, there is lots and lots of significant coverage of Jessa as her own person, quite apart from her family. StAnselm (talk) 06:15, 12 February 2015 (UTC)
 * Weak keep She seems to have a fair bit of independent coverage. Juno (talk) 07:40, 12 February 2015 (UTC)

Please add new comments below this notice. Thanks, Missvain (talk) 05:52, 15 February 2015 (UTC)
 * Keep as per sources above and in article. Meets WP:GNG.--Tomwsulcer (talk) 11:12, 17 February 2015 (UTC)


text:
Dast Feshad

Dast Feshad (, also Romanized as Dast Feshād and Dastfeshād; also known as Dasht Feshād) is a village in Ghazali Rural District, Miyan Jolgeh District, Nishapur County, Razavi Khorasan Province, Iran. At the 2006 census, its population was 182, in 47 families.

title: Dast Feshad


text:
Template talk:suffix

Meta
I think it would be vastly better not to subst this template, nor to use it directly in most cases; it would make the most sense to use it as a meta template for more specific templates like and. -- Visviva 10:54, 7 October 2007 (UTC)

English-only?
Are templates and  supposed to be English-only, and that's the reason why they don't accept lang= parameter (AND use  which seems to be aware only of English POS)?

Same question applies for those inside Category:Suffix templates and Category:Prefix templates, although I see some French stuff there but still without lang parameter and support for alternate text (so that one could link to lemma entry and display a stem). --Ivan Štambuk 00:37, 4 November 2007 (UTC)
 * I removed the and replaced it with the result of, because it is a general template. perhaps a third (or named) parameter can be added if people are desperate to have the  styling. Conrad.Irwin 00:16, 9 November 2007 (UTC)

 * Why not just call with  |lang={{{lang|}}|sc=  ? Then you can use either or both as desired and get whatever customization that term gets you (including section links).

 * If cases are any more complicated (alt links etc), it really ought to be written as foo-stuff + bar-stuff on the page, trying to use this is overkill. It is supposed to just make things easier. Robert Ullmann 00:43, 9 November 2007 (UTC)

 * I delegated the work to, so most of this should be possible. H. (talk) 14:09, 30 October 2008 (UTC)

Minor code modification
I've replaced   call with   . For non-top-40 languages   code gets expanded into wikified version which screws up linking to language sections (compare  with ). It took me a while to figure this out (Special:ExpandTemplates is a great tool!).

Hopefully nothing is broken.. --Ivan Štambuk 20:15, 14 November 2007 (UTC)

Categorization
I would like to categorize pages that use this template with   but I'm not sure if that's the best category name and I don't know how  is supposed to be used. DAVilla 00:11, 25 November 2007 (UTC)

 * That's a great idea! So far explicit categorizing has been used (Category:English nouns ending in -ism for example). {t-sect} is used quite straightforwardly: you just pass it the ISO code of parameter  lang  and it returns language name.

 * A few considerations that should be made:
 * 1) Some prefixes/suffixes are extremely productive in some highly inflective languages. Maybe this categorization should be applied only to lemma forms? If that is the case, than the template shouldn't be used for any of the derived forms, which could potentially have it's own specialized categorization scheme (such as Category:English plurals ending in "-es". That would however degrade the status of non-lemma terms, and how good/bad that is, I don't know, but judging with recent discussions in mind I don't think everyone would be too happy about it. OTOH, generating categories that would contain tens of thousands of bot-generated derived verb forms of Spanish verbs would be an overkill.
 * 2) Prefixes and suffixes could be mutated in various ways, consonants could be lost, assimilated.., and most languages don't use morphological orthography. So if I put that bešuman is built as bez- + šuman, and the template categorizes it in, that would be factually wrong.. --Ivan Štambuk 12:45, 25 November 2007 (UTC)

 * How about Category:English words suffixed with -ism instead, and likewise for all others? DAVilla 06:04, 5 December 2007 (UTC)

 * That would be much more precise wording.
 * Also, this raises the question of Derived terms header entries for affixes, as these categories and entries in those lists should be identical. For some extremely productive suffixes, categories make much more sense. If both are to be kept, this could be an opportunity to automate synchronization of these two. --Ivan Štambuk 15:21, 5 December 2007 (UTC)

Changes in the root
Could there be an extra parameters for instances where the original word changes when suffix is attached (i.e. instead of big + -er one could write big(g)- + -er, or more suitably for agglutinative languages which may have very different roots: mennä + -minen → mene- + -minen)? --Jyril 22:01, 23 March 2008 (UTC)

 * I introduced this, see above. H. (talk) 14:09, 30 October 2008 (UTC)

PoS/Ety link
If arguments 1 or 2 refer to long English entries, the user can miss the relevant etymology or PoS. Would it be possible to allow the arguments to be of the form X to allow for links to the right PoS or at least the right etymology. The same would apply to prefix, of course. DCDuring TALK 15:19, 4 September 2008 (UTC)

 * This is what the ss parameter is for, though I would rather remove it, since it makes the template overly complicated. Instead, a gloss can be used. H. (talk) 14:09, 30 October 2008 (UTC)

 * I have two issues.
 * "ss=" only applies to the suffix. I am trying to help a user with a link to, say, a polysemic verb root which is preceded on its page with a long noun section.
 * Hard-coding section numbers doesn't work well for English, especially for the root words. I expected to be able to insert a piped link for the stem that would have enable me to send a user directly to the relevant etymology or PoS and not have it break every time an etymology, pronunciation, alt spelling, translation, semantic relations, usage notes, or PoS section is added or an errant "Homophones" header is excised. A named section link is less likely to break. DCDuring TALK 14:59, 22 July 2009 (UTC)

From
I added the word ‘From ’ in front of the template. This reflects the majority of the uses of it, namely plainly in the etymology section with not context. But that is too concise in my POV. This will break some pages, but I did some random tests on referring pages and most of them are fine. Maybe we could add an optional nofrom= parameter which would indicate the from should not be there, if people think it is needed, although I like the uniformity. H. (talk) 09:22, 23 September 2008 (UTC)

 * Reverted (by Robert) as change was not discussed and the template is used widely (breaking many existing usages). See Beer parlour. --Bequw → ¢ • τ 06:35, 25 September 2008 (UTC)

Parameters sc= and tr2=
The above parameters don't work. See ծանրություն or учитель, for example. I don't have much experience in template editing, so can someone fix this please? --Vahagn Petrosyan 05:57, 1 April 2009 (UTC)
 * Now fixed. Conrad.Irwin 14:00, 2 April 2009 (UTC)
 * Fantastic. Thank you very much. Can you do the same for and ? It must be analogous, right? In  gloss1= doesn't work and sc=, tr1=, tr2= do not exist. In  sc=, tr1=, tr2= do not exist.   --Vahagn Petrosyan 07:46, 3 April 2009 (UTC)

Fix categories for rtl?
Trying to use this for things like Hebrew, the page displays properly, but the category comes up "Hebrew words suffixed with -י" with the hyphen on the wrong end of the suffix. I tried to fix this once, but got impatient pretty quickly. Could there be a way to fix it? — [ R·I·C ] opiaterein — 11:38, 5 July 2009 (UTC)

 * Well, I got that to work. At some point I want to find out if Arabic has a specific unicode symbol so I can add languages that use the Arabic script. etc. — [ R·I·C ] opiaterein — 20:30, 25 July 2009 (UTC)

params t1, t2
I added parameters t1, t2 as alternatives to gloss1, gloss2 for the sake of "consistency" with. AugPi 13:08, 20 September 2009 (UTC)

suffixes sandwiched between two hyphens
If a suffix is sandwiched between two hyphens, e.g. -ad-, then use parameter <tt>infix=yes</tt> as in vojaĝado. The alternative is to include the right hyphen in parameter 2. AugPi 21:26, 8 November 2009 (UTC)

Multiple suffixes
Could there be an option to indicate multiple suffixes, if no intermediate one-suffix form exists? Nesting this template does not seem to work. --Tropylium 09:15, 11 February 2010 (UTC)
 * You can do a trick like this. --Vahagn Petrosyan 09:48, 11 February 2010 (UTC)
 * In Esperanto, I am dealing with multiple suffixes rather frequently. Appending all those s gets rather ridiculous when etymologizing a word like . It would be much preferable if suffix could handle three or four suffixes at once. - Robin 12:12, 22 September 2010 (UTC)
 * The Hungarians might have a language-specific template, not so picky about "-"s, that could be copied and modified. DCDuring TALK 13:32, 22 September 2010 (UTC)

POS cat
Since apparently "words" isn't specific enough (see Category:Portuguese adverbs suffixed with -mente) could someone add a pos= option to this bad boy? — [ R·I·C ] opiaterein — 22:53, 3 May 2010 (UTC)

Japanese and Korean affixes
A while ago we decided not to use hyphens with Japanese and Korean (except when in Roman letters), both kana and kanji, at the BP. Is it possible to edit this template so that it reflects this change? I can take a look at it myself but I thought somebody else knows how the template works and could make the edit easily. TIA Haplology 13:28, 11 November 2011 (UTC)

 * Yes, it's possible, but the categories will need to be fixed at the same time, and will have to be changed accordingly. And you'll probably want to make the same change to  and  and prefix-categories. The smoothest way to do it is probably:
 * Create the new suffix-categories.
 * Update and . (I've created  and, which you can steal. I haven't tested them, but I think they're good.)
 * Delete the old suffix-categories.
 * Repeat, this time for prefixes.
 * —Ruakh TALK 21:14, 11 November 2011 (UTC)
 * Thanks, I'll do that. I've started on step one. Fifty some categories to go.  Haplology 16:22, 12 November 2011 (UTC)
 * Made the new categories, updated  and , and all seems to be well except that the new categories still throw up an error message, for example Category:Japanese_words_suffixed_with_%E7%95%8C. I'm deleting the old categories now.  Thanks for helping me through this! Haplology 18:20, 12 November 2011 (UTC)
 * Re: error message: oops, fixed, thanks! —Ruakh TALK 18:43, 12 November 2011 (UTC)

Usage with proto-terms
How it is supposed to be used? It generates weird category name. --Ivan Štambuk (talk)
 * It works normally when both positional parameters are provided. However, it is broken when the first positional parameter is left empty. --Ivan Štambuk (talk) 08:37, 12 August 2013 (UTC)
 * That's only if it's placed on the start of a line. But why would you want the line to begin with " + ..."? 12:05, 12 August 2013 (UTC)

Performance
Why does this template often fail to give me the font that I expect (for English) when, on the same line, does? Is term that much simpler? In what way? Can this defect be remedied by making if function more directly. DCDuring TALK 16:06, 18 September 2013 (UTC)
 * This template actually uses, so that is not the problem. 17:32, 18 September 2013 (UTC)
 * Is it the extra delay of calling it? What is that delay? Does something start executing before some lower-level functional relating to fonts is complete so a default is not overridden? ?
 * @CodeCat: This template doesn't literally use ; they both ultimately call the same Lua function, of course, but there's also a good chunk of duplicated/unshared code in setting up the arguments to that function, and hence opportunity for discrepancies and -specific problems. —Ruakh TALK 23:49, 18 September 2013 (UTC)
 * But I notice that the problem is not what I thought it was. The desired font (I think: it happens fast) appears and then, for some templates, apparently those that use Lua, the font is converted to another font.
 * Are we sure that we want to fight this Webfont/ULS stuff? DCDuring TALK 00:02, 19 September 2013 (UTC)
 * and both use Lua. (BTW, if you're asking CodeCat/me/anyone to investigate, I think you should link to an example, and/or give steps to reproduce. Otherwise this discussion won't really go anywhere.) —Ruakh TALK 00:59, 19 September 2013 (UTC)

- result of - this time with sans serif font

- result of - this time with serif font

- result of - this time, as always, with sans-serif font

- result of - this time, as usual, with serif font.

Is the result pattern similar for others? DCDuring TALK 01:10, 19 September 2013 (UTC)
 * That's odd, considering has the "sans-serif" style from Latn-mention, while  has no such declaration. Either way I can see no difference between your examples. DTLHS (talk) 01:27, 19 September 2013 (UTC)
 * And I'm guessing this has something to do with the fact that automatically assumes English (lang="en") while  has no such assumption (lang="und"). DTLHS (talk) 01:36, 19 September 2013 (UTC)
 * Could well be. does not use any font or language templates or modules.  uses just, AFAICT. DCDuring TALK  01:43, 19 September 2013 (UTC)
 * Do you see the quotation arrows at Croton? I don't.
 * I am ready to try almost anything, but I am discouraged that even a FF "private window" and cleared caches gave only brief, temporary from any of the symptoms. DCDuring TALK 01:43, 19 September 2013 (UTC)
 * No, everything looks fine to me. DTLHS (talk) 01:50, 19 September 2013 (UTC)

Suffix to a word from a foreign language?
I have a slight issue with this template. The problem is that I cannot appropriately describe adding a suffix to a transcription of a foreign word. What I'm talking about is something like larpurlartizam. "Larpurlart" doesn't exist as a word itself in Serbo-Croatian, it is a respelling of the French "l'art pour l'art" and the suffix -izam is appended onto that. However, if I add the "lang=sh" option to the template, the link to l'art pour l'art (art for art's sake) includes the index code for Serbo-Croatian (https://en.wiktionary.org/wiki/art_for_art%27s_sake#Serbo-Croatian).

Is there a way to address this issue while still having the word "larpurlartizam" automatically added to the category "Serbo-Croatian words suffixed with -izam"? <IP_ADDRESS> 14:26, 27 October 2013 (UTC)

 * Nevermind, I'm silly. All I had to do was write "l'art pour l'art" separately and leave the first entry in the suffix template empty. <IP_ADDRESS> 14:38, 27 October 2013 (UTC)

Suppress plus sign
Sometimes you don't want the plus sign, e.g. when there's some explanation and you write "suffixed with -xy" or the like, then "suffixed with + -xy" is awkward. Could we add a parameter "noplus=1"? Or is there already a way to suppress it? <IP_ADDRESS> 18:31, 2 April 2021 (UTC)

title: Template talk:suffix


text:
Marko Asmer

Marko Asmer (born 30 July 1984) is an Estonian racing driver, who won the British Formula 3 Championship title in 2007. Asmer is also the first Estonian to test a Formula One car, having tested for the Williams BMW team in 2003, after just half a season of car racing in British Formula Ford. Asmer's father is a former racing driver Toivo Asmer, who was Estonian Minister of Regional Affairs between 1999 and 2003.

Racing career
Asmer was born in Tallinn. His father is motorsports promoter, musician and politician Toivo Asmer. He began karting in 1995, aged eleven, and had won the Estonian, Baltic, Finnish and Scandinavian kart championships by 2001. Asmer went on to make his car racing debut in 2003 and raced in British Formula Ford for team JLR. He scored six wins that season and finished in second place in the Formula Ford festival. Apart from a brief participation in the Formula Renault V6 Eurocup in 2003, Asmer's career was henceforth focused on Formula Three in Britain and Japan. He made his British series début in 2004 with Hitech Racing and, apart from a move to Japan in 2006, he has remained with the team in the years since. He became a championship title contender on his return to the British series in 2007, led the points standings for most of the season, and secured the title at Croft with three races remaining. His participations in All-Japan F3 have been confined to one and a half seasons with Three Bond Racing in 2006 and 2007, the latter of which was limited by competing in Britain. In 2008 Asmer was BMW Sauber's second test driver alongside Christian Klien and competed in seven of ten rounds in the GP2 Series for FMS International.

Retirement
Following the conclusion of the 2008 GP2 season Asmer parted ways with Fisichella Motor Sport and was unable to find a new team in GP2 for the 2009 season. Due to new rules restricting the amount of testing Formula 1 teams could carry out in-season he also lost his role as test and reserve driver for the BMW Formula 1 Team. With no competitive race seat for the 2009 season Asmer became a test and reserve driver in Superleague Formula series.

On 8 April 2010 Toivo Asmer, the father of Marko Asmer, announced that Marko had ended his career in motorsport he had no race seat or test/reserve driver role for the 2010 season, and lack of funding meant that his son's career was finished. Despite this Asmer made a quick return to the cockpit the following week when he tested for the Atech team in a GP3 Series test session in Barcelona.

Return to competitive racing
In February 2011 Asmer returned to motorsport when he tested a British Formula 3 car for the Double R Racing team at Silverstone, during which he set competitive times. Staying with Double R Asmer finally returned to competitive racing when he competed in the Pau Grand Prix on 21–22 May 2011. Asmer qualified 10th and after a bad start found himself in last place, but showed good race pace and overtaking nous to finish 7th.

Following his return to racing Asmer was interviewed by Autosport.com and revealed that he had spent his time out of professional motorsport "testing some cars, doing karting and ... doing some driver coaching". He went on to say that he had no firm plans for the future, although he did want to take part in the Macau Grand Prix. Asmer also said that he would welcome a return to racing "if something good comes up", although a full-time return to British F3 would not interest him.

Despite these claims it was announced on 28 July 2011 that Asmer would return to British Formula 3, again racing a Dallara-Mercedes for the Double R team at the Spa-Francorchamps round. Asmer qualified 18th (of 28 cars) for Race One at Spa, but then scored Double R's best qualifying result of the season, lining up second on the grid for the Feature Race. Asmer failed to finish in Race One or Two, but drove solidly to finish sixth in the Feature Race. However, his status as an invitational driver meant that he was not eligible to score championship points for this weekend. During this weekend it was also announced that Asmer had sponsorship in place to take part in the 2011 Macau Grand Prix, where he would drive a Dallara-Mercedes for a three-man Double R Racing team, alongside GP3 champion Valtteri Bottas and current GP3 Series racer Mitch Evans.

In an interview with Autosport carried out over the Macau Grand Prix weekend Asmer reiterated his desire to get back into racing full-time, and said his future may lie in DTM.

Return to regular racing
In recent years Asmer has returned to actively racing in competitive international motorsport. He raced as part of a four-man team alongside Formula 2 race winner Kazim Vasiliauskas, driving a McLaren MP4-12C GT3 in the 2014 24 Hours of Spa with the GT Russian Team. He also competed in several rounds of the ADAC GT Masters. Asmer continued to race for GT Russian Team, taking part in the 2015 Blancpain GT Series (the successor to FIA GT1 World Championship), with his best result being a 7th-place finish in the main race in the final round in Zandvoort. He also raced in the top A6 category of the Dubai 24 Hour, again for the GT Russia Team.

Motorsport management
Since summer 2020 Marko Asmer is the manager of Estonian racing driver Jüri Vips.

Complete GP2 Series results
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)

title: Marko Asmer


text:
Wikipedia:WikiProject Spam/LinkReports/respon4d.com

Links

 * respon4d.com resolves to [//<IP_ADDRESS> <IP_ADDRESS>]
 * Link is not on the blacklist.
 * Link is not on the domainredlist.
 * Link is not on the Monitorlist.
 * None of the mentioned users is on the blacklist.
 * Link is not on the whitelist.
 * Link is not on the monitor list.
 * Link is not on the whitelist.
 * Link is not on the monitor list.

Users
No users found.

Additions
No additions recorded.


text:
Field Guide

 * Animal Tracks
 * Bats
 * Birds
 * Clouds
 * Constellations
 * Frogs
 * Insects
 * Beetles
 * Butterflies and Moths
 * Caterpillars
 * Dragonflies and Damselflies
 * Mammals
 * Mushrooms
 * Newts and Salamanders
 * Reptiles
 * Rocks and Minerals
 * Scat
 * Scorpions
 * Sea Mammals
 * Sea Shells
 * Sharks
 * Snakes
 * Snakes of Europe
 * Spiders
 * Plants
 * Cacti
 * Edible Wild Plants
 * Mosses
 * Lichens, Liverworts, and Mosses
 * Trees
 * Wildflowers

title: Field Guide


text:
Sugaryn Gan-Erdene

Sugaryn Gan-Erdene (Сугарын Ган-Эрдэнэ; born 12 March 2003), is a Mongolian chess player. He is an International master since 2019. He is ranked 8th player and best U18 player in Mongolia. He is ranked 16th U18 player in Asia.

Career
Gan-Erdene played in the U-10 section of the 2013 World Youth Chess Championship, finishing on 7.5 points out of 11.

He played in the Chess World Cup 2019, where he was defeated by Ian Nepomniachtchi in the first round.

title: Sugaryn Gan-Erdene


text:
Lamplough, Victoria

Lamplough is a locality near Avoca, Victoria in Australia. It was the site of a gold rush from November 1859 and up to 16,000 people were on the site. The lead was worked for a distance of nearly 3 miles (5 km) to the point where it ran into the water and was abandoned.

Gold history
In August 1859, the Mining Surveyor at Maryborough reported Lamplough as a "grand attraction; hundreds of miners are arriving daily from the more remote gold-fields. The yield of gold,together with the large extent of the already proven auriferous ground, indicates that the Lamplough presents every appearance of being the largest rush we have yet had in Victoria."

In January 1860, the surveyor reported that "Lamplough may safely be classed amongst the permanent and payable gold fields of Victoria". He did note that the field was overpopulated, particularly by those in business pursuits: "there appears to be nearly one place of business to each miner’s tent". In March 1860, the surveyor reported: "Lamplough, during the last few weeks, presents the appearance of one of the settled gold fields. The late departures to the Inglewood rush have materially improved its condition by withdrawing a portion of its surplus population, such as unsuccessful miners, storekeepers, &c. It may safely be presumed that those now remaining are all making at least a good livelihood".

In June 1860 he reported: "At Lamplough, the Deep Lead (with the exception of minor rushes in the immediate neighbourhood) offers sufficient inducements to remain. The lead appears still to adhere (as originally) to the southern reef, neither do the workings get into deeper or wet ground. It has been found payable more than two miles in length from the original prospectors’ claim, and three claims in width, the average yield being an ounce to the load, with one foot thickness of wash-dirt".

July 1860: "The Lamplough Deep Lead is steadily progressing. Several other shallow workings upon adjacent hills, and many of the neighbouring gullies, are being prosecuted; but, from what I can ascertain, are only attended with wages results. The population at Lamplough is rather on the increase, principally from Inglewood. A new rush occurred a few days ago about eight miles from Lamplough, on the Lexton road; but in the absence of any payable ground (except the prospectors) having been discovered, it has nearly subsided again".

September 1860: "At Lamplough I cannot note any material change in mining since my last. Several of the small rushes in the immediate vicinity appear to give remunerative employment to a large number of miners whilst water for washing purposes is easily obtained; but in the absence of any natural or artificial means for securing it in this dry part of the district, and that when the present supply is exhausted, I predict a considerable decrease in their numbers will result".

In November 1860: "Lamplough (with occasional small rushes, either to the deep lead or to the immediate vicinity) still retains its population."

In January 1861, the report was quite different: "The population at the new diggings (Mountain Creek) is yet daily increasing, and from the fact of payable ground having already been found extending over a large area, together with new discoveries of frequent occurrence, .... Lamplough, and all the other sections of my division (in consequence of this rush), are now quite denuded of their European alluvial mining population".

In March 1864, 160 alluvial miners were reported to be working at Lamplough of a total of 1,605 miners working within the Avoca Division. This number remained fairly steady until the end of 1866 and in 1867 shrunk to 70 miners. In 1869, a company was mining in the area.

Next gold rush
The next rush was to Moonambel, then known as Mountain Creek at the end of the Pyrenees Ranges, north of Avoca. Other miners moved to Kiandra, New South Wales and to New Zealand where there is a Lamplough Lead just north of Hokitika.

Post office
Lamplough Post Office opened on 1 January 1860 and closed in 1970.

Significant events
The Avoca and District Historical Society has documented a number of significant events in the Lamplough region.

title: Lamplough, Victoria


text:
Philip "Little Farvel" Cohen

Philip "Little Farvel" Cohen alias Jack Kofsky (1906 or 1907 – September 15, 1949 ) was a figure from organized crime in New York in the 1930s, now considered a member of the so called Kosher Nostra. According to the authorities, Cohen, a former rackets collector, was a member of the criminal organization Murder, Inc., led by Louis Buchalter and, like the gang leader and other members of the organization, was involved in international drug trafficking.

International drug trafficking
According to the findings of the Federal Bureau of Narcotics (FBN), the international drug trade intended for the USA in the 1920s and 1930s was largely controlled by Jacob Katzenberg, who was based in New York City. This supplied a large number of criminal gangs, including the organization around Louis Buchalter, to which Philip Cohen also belonged, with opium, which was initially obtained from Europe and later directly from China and then sold on nationally in the USA. The many murders carried out by Cohen's organization, which the press dubbed Murder, Inc., were largely based on enabling and covering up crimes of the criminal organization and the National Crime Syndicate, such as the drug trafficking organized by Katzenberg. This was actively supported by Murder, Inc. and can be seen as one of the main sources of income for the criminal organization in addition to the infiltration of unions and related industries - such as in particular the clothing industry in the Garment District (Manhattan).

Philip Cohen and his accomplice Emanuel Weiss were heavily involved in the criminal organization's drug deals. The FBN first became aware of the group's machinations in 1935 when the remains of an opium processing plant were discovered by authorities after an explosion in a residential building on Seymour Avenue in New York City. In 1937, the FBN believed it had secured evidence of a violation of the US Narcotics Act by Cohen and Weiss when they managed to find Jacob Gottlieb at Rouses Point in New York State with a suitcase full of heroin. When he was arrested, he told the authorities that he had smuggled drugs from France through Canada to the USA for Cohen and Weiss and that the two were his clients. Shortly afterwards, while still in custody, Gottlieb committed suicide by hanging himself in his cell for fear of retaliation by Murder, Inc. against him or his family. No charges could be brought against Cohen and Weiss due to the death of the only witness.

In 1939, the two Murder, Inc. members, who had long been the focus of the FBN, were finally indicted for violations of the US Narcotics Act. During a house search, FBN investigators discovered a chemical plant used to stretch morphine and had secured evidence of the involvement of Weiss, Cohen and three other people named Samuel Bernstein, Abe "Little Yiddel" Lorber and Al Angelson. After the fugitives were arrested in 1939, the trial was scheduled for 1940. Emanuel Weiss and Philip Cohen were released after paying bail, but did not appear at the trial because they had also been charged with the murder of Joseph Rosen, a former haulage owner, since May 1940 and wanted to evade the trial.

After several months of manhunt, New York police officers managed to arrest Cohen in a Brooklyn apartment during a nightly house search on November 30, 1940, and found the wanted man exhausted and under the influence of drugs. There was no sign of his accomplice Weiss. In February 1941, Philip Cohen and the three remaining defendants were sentenced to three to ten years in prison. Cohen was sentenced to ten years.

Murder of Joseph Rosen
In the mid-1930s, prosecutor William O'Dwyer, who had set himself the goal of taking action against organized crime, put the focus of his investigation on Louis Buchalter, the boss of Cohen. This resulted in particular in driving potential witnesses out of town or their being murdered. Buchalter saw danger in a businessman named Joseph Rosen, who had been informed of the gang leader's involvement in the infiltration of the unions and had returned to the city against his will. On September 13, 1936, on Buchalter's orders, Rosen was shot in his shop in Brownsville, New York City. Harry Strauss was supposedly commissioned with the planning and execution of the crime along with James Ferraco, Emanuel Weiss, Sholem Bernstein and Louis Capone. Along with Sholem Bernstein, Philip Cohen was seen as an escape driver and is said to have transported the perpetrators, who initially used a stolen escape vehicle, in his car after leaving the vehicle and helped them escape from the crime scene. When the public prosecutor's office was able to prosecute those involved on the basis of the testimony of the contract killer Abe Reles, who had become an informant, Philip Cohen was initially included in the murder charge in 1940, but was later struck off the list of accused due to lack of evidence. Instead, he had already been convicted of drug smuggling. Cohen's accomplices Emanuel Weiss, Louis Capone and gang leader Louis Buchalter were sentenced to death for the murder of Rosen and in 1944, after two years of vehement but unsuccessful attempts to enforce a retrial, were executed in the electric chair in Sing Sing Prison.

Murder of Danny Fields and Louis Cohen
Philip Cohen was also linked by investigators with the FBN to the double homicide of Danny Fields aka Isadore Friedman and Louis Cohen on January 28, 1939, and is believed to have been one of the shooters. However, in the absence of sufficient evidence, no charges could be brought against Cohen.

Assassination
Philip Cohen was found dead on a Long Island road a few months after his release on September 15, 1949. He had been shot in the head four times. The authorities ruled out robbery and rather classified the act as a classic underworld-style execution; the perpetrators had no interest in various valuables that Cohen was carrying. Police officers later found Cohen's car with traces of blood on the passenger seat. Allegedly, Cohen was murdered in a manner similar to that of several Murder, Inc. victims who were shot dead by a perpetrator sitting behind them during a final drive. However, prosecutor Burton Turkus, who served in the Joseph Rosen murder case, contradicted claims in the press that Cohen may have been murdered in retaliation for the conviction and execution of Louis Buchalter, Emanuel Weiss and Louis Capone to avoid the electric chair himself. In fact, Cohen never cooperated with the authorities, said Turkus. In typical underworld fashion, the accused kept silent about any offers made by the public prosecutor. The day Cohen was released from the dock for lack of evidence, he turned to Buchalter in the courtroom and assured him that he had not cooperated nor would cooperate. The police failed to solve Cohen's murder. It was assumed, however, that after his release from prison, Cohen wanted to gain a foothold in the criminal milieu again and thereby pushed competitors out of their niche. In particular, Cohen, as the head of a criminal group, is said to have tried to blackmail betting shops and accountants.

title: Philip "Little Farvel" Cohen


text:
Wikipedia:WikiProject London Transport/Recognised content/bot list/GTbotlist

List of London Monopoly locations

Total pages in content type is 1


text:
Talk:Circle of confusion computation

Comment from article
 -Splash - tk 23:49, 20 October 2006 (UTC)

What follows is a computation of the Circle of confusion in Wiki format using "modern" notation and showing all of the steps.

(NOTE: Some of the symbols may be poorly chosen, as the original author is not intimately familiar with the conventions used in the optics literature. Wiki's are for fixing, right?  The author can provide the Visio source for the diagram.)

Why?
I'm unclear on the point of this article. What is the so-called "modern" notation? Why can't this calculation, maybe less belabored, go into one of the existing articles, using notation consistent with them?

It ends up with "This confirms the assertion in the Depth of field entry that the depth of field is a function of the actual aperture size, independent of the sensor size," but I don't find the referenced assertion when I search for "independent" on that page. What exactly was the assertion, and how does the notation of this page confirm it?

Dicklyon 03:00, 11 August 2006 (UTC)

Why not?
I found the JPEG's from 1866 difficult to follow, and I failed to find a clearer derivation after searching the Internet for quite some time. There ought to be a link to something like this from the CoC page; if you have a better reference, then go ahead and change the link. <IP_ADDRESS> 14:35, 11 August 2006 (UTC)

 * Why not do it up concisely on the COC page, with notation taken from depth of field and/or hyperfocal distance? There's nothing modern about using B for COC diameter. Dicklyon

"This difference between formats goes away if the cameras are compared with equal aperture diameters rather than equal f-numbers" <IP_ADDRESS> 14:35, 11 August 2006 (UTC)

 * I thought that might be it. I wrote that, in a context where I think it was more clear what was meant.  I would never say the DOF is independent of sensor size, though, as it assumes too much about what you mean about the other variables. Dicklyon

I think the last sentence of this article should be removed, because it's at least strongly misleading. I just had a discusson on an other forum, where someone referred to this article's last sentence to "prove" that DOF is in deed independent from format size... Szeder 14:16, 9 October 2006 (UTC)

 * Well you're right that it's misleading, or even downright wrong. But the whole article is so messed up it's hard to see how to work on it incrementally.  I'd start with a new figure... Dicklyon 16:28, 9 October 2006 (UTC)
 * So I took it ouk. The article is still pretty bogus, with strange terminology, complex equations, and results in a form that is hard to interpret.  I'm not even sure it's right, and the approximations certainly limit its domain of applicability.  It would be easier to redo using magnification and the blur circle in the field plane, but it would mean starting over with a drawing, new terms, and all new equations. Dicklyon 05:07, 10 October 2006 (UTC)

Recommend for deletion?
I don't think this article can be rescued, or has any point. I intend to recommend it for deletion unless someone objects and volunteers to work on it. Dicklyon 05:12, 10 October 2006 (UTC)

Done. Listed AfD. Dicklyon 04:19, 11 October 2006 (UTC)
 * I am in favour of keeping the information. It is useful, but needs more work. --Thorwald 05:01, 11 October 2006 (UTC)

Articles for Deletion debate
This article survived an Articles for Deletion debate. The discussion can be found here. -Splash - tk 23:49, 20 October 2006 (UTC)

 * Huh? What do you mean by survived?  Looks to me like the consensus was delete, but add a bit about it into the other article.  Shouldn't we then at least have a merge tag? Dicklyon 00:09, 21 October 2006 (UTC)

 * OK, since the consensus seems to have been to delete the article but merge its contents into circle of confusion, I did so, with a new diagram and a greatly simplified derivation. Only trouble is that my arrowheads from Inkscape disappeared, so if anyone knows how to fix this, please say so or just do it. Dicklyon 18:42, 22 October 2006 (UTC)

 * I got the arrowheads back by "stroke to path" conversion. Dicklyon 21:13, 22 October 2006 (UTC)

title: Talk:Circle of confusion computation


text:
User:Arliu2005/Books/Religion: Christianity

Religion: Christianity

 * Christianity
 * Jesus
 * Christ
 * Son of God
 * Messiah
 * Jesus in Islam
 * Crucifixion of Jesus
 * Resurrection of Jesus
 * Second Coming
 * Gospel
 * List of Gospels
 * Gospel of John
 * Old Testament
 * New Testament


text:
Old Post Office (Augusta, Maine)

The Old Post Office and Court House is a historic former federal government building at 295 Water Street in downtown Augusta, Maine. Built in 1886-1890, it is one of Maine's finest surviving examples of Romanesque Revival architecture. It was listed on the National Register of Historic Places in 1974.

Design and construction
The former Post Office and Court House stands on the east side of Water Street, Augusta's principal commercial downtown thoroughfare, at the southeast corner with Winthrop and Front Streets. It is a symmetrical 2-1/2 story granite structure with a central tower, flanked on either side by a wall and smaller tower. It was designed by Mifflin E. Bell (1846-1904), the Supervising Architect for the U.S. Treasury. Bell's term ended July 1887, and his successor William Alfred Freret finished the job, and the building opened in January 1890. The cost of construction was $178,281.20. It contained 427,600 cubic feet, was heated by steam, and contained a hydraulic freight elevator for post office use.

The building was enlarged sometime during the tenure of treasury architect James Knox Taylor (1897 to mid-1912).

History
The building was used as a courthouse and post office until the 1960s, when a new, larger federal building was constructed for these uses. The Old Post Office was sold as surplus property to a private owner. It was adaptively repurposed to house a bank, restaurant, and office, while largely preserving the exterior.

title: Old Post Office (Augusta, Maine)


text:
Calderpark Halt railway station

Calderpark Halt railway station or Calderpark for Glasgow Zoo (NS679625) served Calderpark Zoo opened in 1947 on the old estate of Calderpark and the Baillieston area of Glasgow, Scotland on the Glasgow, Bothwell, Hamilton and Coatbridge Railway between Shettleston and Hamilton. Glasgow Zoo closed in 2003.

History
The halt was opened by the British Transport Commission to serve Glasgow Zoo in 1951 on the Glasgow, Bothwell, Hamilton and Coatbridge Railway route by Mrs Cameron wife of British Railway's Chief Regional Officer for the area.

The route was also known as the London and North Eastern Railway's Hamilton Branch. It was closed when the line was closed to passenger traffic on 4 July 1955. The line was closed to freight traffic on 4 October 1964.

Infrastructure
The halt had a name board that read 'Calderpark for the Zoo', had electric lighting, two concrete platforms with simple brick built shelters and toilets on the northern side with sloping concrete roofing on a double track section of track standing just to the west of the North Calder Viaduct. The Calderpark Viaduct lay to the west. The remains of the halt on the dismantled line are shown with two shelters on the south side of the line in a low cutting just off Baillieston Road.

Remains on site
Glasgow Zoo closed in 2003 and eventually the buildings were demolished and replaced by a housing estate (part of Broomhouse). The site of Calderpark Halt has become Calderpark Terrace and the only remains are at the site of the old North Calder Viaduct.

title: Calderpark Halt railway station


text:
Talk:COMUSNAVCENT

Usage
"Beginning in February 2000, the U.S. Naval Forces Central Command (COMUSNAVCENT) instituted a weekly DNBI incident morbidity surveillance system for all ships within its 'Area of Responsibility' (AOR) which constitutes waters and littoral areas of the Arabian Gulf, Gulf of Aden, Gulf of Oman, Red Sea, Arabian Sea and northwest Indian Ocean." Published online 2006 February 25. doi: 10.1186/1471-230X-6-9.
 * Riddle, Mark S. et al. Epidemic infectious gastrointestinal illness aboard U.S. Navy ships deployed to the Middle East during peacetime operations – 2000–2001 BMC Gastroenterol 2006; 6: 9.

"The attached comments from GENICOM, PACOM, and the Navy (CINCPACFLT, COMUSNAVCENT, CINCUSNAVEUR and CINCLANTFLT) note operational benefits provided by ..."
 * US General Accounting Office 1988 ''Navy Aircraft Carriers: Cost Effectiveness of Conventionally and Nuclear Powered Carriers.

"COMUSNAVCENT     Commander, U. S. Naval Forces, Central Command"
 * Head, William P. and Tilford, Earl H. (1991) The Eagle in the Desert: U. S. Naval Involvement in in the Persian Gulf War Praeger. Abbreviations and Acronyms, p. xiv.

COMUSNAVCENT
Any takers? Pretty sure it's not a noun. SemperBlotto 08:22, 3 October 2007 (UTC)

 * It certainly *looks like* a US Navy abbreviation. Maybe "Central Command U.S. Navy". Is it real? DCDuring 14:57, 6 October 2007 (UTC)

 * My guess as to meaning seems right. It is readily findable at official military websites. Isn't that enough? If not, it ought to be possible to find newspaper references to it. DCDuring 15:10, 6 October 2007 (UTC)

 * I have posted 3 usages from on-line copies of hard-copy documents: 1 refereed journal, 1 govt. report (non-DoD), 1 book; spanning 18 years. The book citation is just a single line from a glossary. DCDuring 16:43, 6 October 2007 (UTC)

title: Talk:COMUSNAVCENT


text:
Talk:BiPu

Unfortunate word mixing
Do people think it is wise to mention the words emergency sanitation and open-bottom in the same short paragraph?--Light current 22:56, 27 March 2006 (UTC)

 * lol I didn't think of that. I'll reword. --Singkong2005 03:48, 11 May 2006 (UTC)

title: Talk:BiPu


text:
Talk:David Byrne (barrister)

Fair use rationale for Image:David Byrne EC.jpg
Image:David Byrne EC.jpg is being used on this article. I notice the image page specifies that the image is being used under fair use but there is no explanation or rationale as to why its use in this Wikipedia article constitutes fair use. In addition to the boilerplate fair use template, you must also write out on the image description page a specific explanation or rationale for why using this image in each article is consistent with fair use.

BetacommandBot 10:27, 27 October 2007 (UTC)

title: Talk:David Byrne (barrister)


text:
Matan Kahana

Matan Kahana (מַתָּן כַּהֲנָא, born 29 July 1972) is an Israeli politician who served as deputy Minister of Religious Services and as a member of Knesset for New Right and Yamina. He was an officer in the IDF with the rank of colonel, who served as a fighter in Sayeret Matkal, and as a fighter pilot in the Israeli Air Force. He was a commander of a squadron of F-16s. After retiring from the army, he joined the New Right party, which is part of the Yamina alliance. In 2022 he joined the National Unity alliance.

Currently Kahana serves as a Knesset Member for the National Unity Party.

Biography
Kahana was born in Haifa.

When he was three months old, he moved with his family to New York, USA, following his father's electrical engineering and business administration studies. When he was three, the family returned to live in Moshav Beit Gamliel. Kahana attended elementary school at Kibbutz Hafetz Haim (grades 1-8), and then at the Netiv Meir Yeshiva. In his youth, he was a counselor in the Bnei Akiva movement, in the branch in Moshav Beit Gamliel.

He graduated with a BA in Law at Bar-Ilan University.

Kahana is married to Lisa, a Doctor of Clinical Psychology, and is the father of four children. He lives in the religious moshav Beit Gamliel.

Military career
Kahana was drafted into the flying course, but signed a waiver to serve in Sayeret Matkal. He served as a fighter for three and a half years. In January 1994, when he finished his mandatory service, he joined a fighter pilot course, and served as a fighter pilot in 116 Squadron.

Throughout his service, he participated as a pilot in Cast Lead, Operation Pillar of Defense, and the 2014 Gaza War. He also participated as an F-16 pilot in the Second Lebanon War.

Upon completion of his position as commander of the Valley Squadron, he was promoted to the rank of lieutenant colonel and appointed the head of the division at the Air Force headquarters. In August 2018, he was released from the IDF.

Political career
After his release from the IDF in 2018, Kahana served as director of the Diaspora Initiative at the Center for Educational Technology.

On 10 January 2019, he announced that he was joining the New Right party, led by Naftali Bennett and Ayelet Shaked. He placed fourth on the Knesset party list for the April 2019 Knesset elections, but was not elected to the Knesset after his party narrowly failed to pass the election threshold.

Ahead of the September 2019 elections, he was listed seventh on the Yamina joint party list (on behalf of the New Right). The list won seven seats, and he was elected to the 22nd Knesset.

In May 2022, he resigned from his post of the Religious Services Minister and stated he would return to the Knesset to serve as a Yamina MK, replacing MK Yomtob Kalfon. The move was meant to “help strengthen the coalition.” Following his resignation, Kahana was quickly made the Deputy Religious Services Minister while the coalition government attempted to have him appointed back to his former post through a vote in the Knesset. This was however scuttled by rebel Yamina MK Idit Silman, who voted with the opposition.

In August 2022, Kahana decided to leave Yamina for the National Unity alliance. Kahana's term as the Deputy Religious Services Minister came to an end on 16 August, when the legal mandate for Bennett, who was serving as the acting minister of the department, came to an end after three months.

title: Matan Kahana


text:
Autonomous navigation

Autonomous navigation could refer to :

 * Autonomous aircraft
 * autonomous navigation for spacecraft, e.g. the Autonav on Deep Space 1
 * autonomous navigation of robots (including planetary rovers); see
 * autonomous navigation of ships or watercraft, see Unmanned surface vehicle
 * autonomous proximity operations, e.g. spacecraft rendezvous

title: Autonomous navigation


text:
User:Cindiplace

I am currently working on an online Wikipedia and Libraries course which, I hope, will help me use Wikipedia and allow me to incorporate the use of Wikipedia by our library patrons.

''I, Cindiplace, am an employee of the Boyne District Library, a non profit library dedicated to serving the Boyne City City and global communities, and helping to provide broad access to library resources. I will not make any edits that would not be beneficial to the goals of Wikipedia. While my editing is sort of all over the map, I do like to improve access to important, free, scholarly sources held in libraries and archives.''

I do, from time to time, insert links or create articles based on library resources.

''I will modify my editing behavior based on problems cited by other editors or if my editing conflicts with other Wikipedia guidelines. I ask that other editors do not hesitate to contact me, via my user talk page, if I appear to be going against this declaration.''

title: User:Cindiplace


text:
The Shadow of Chikara

The Shadow of Chikara (also known as Demon Mountain, The Ballad of Virgil Cane, Thunder Mountain, Wishbone Cutter, and The Curse of Demon Mountain) is a 1977 American Western horror film written and directed by Earl E. Smith. The film stars Joe Don Baker, Sondra Locke, Ted Neeley, Dennis Fimple, John Davis Chandler, Linda Dano and Slim Pickens. It was released on July 15, 1977, by Howco International Pictures. The film features the song The Night They Drove Old Dixie Down by The Band.

Cast

 * Joe Don Baker as Wishbone Cutter
 * Sondra Locke as Drusilla Wilcox
 * Ted Neeley as Amos Richmond
 * Dennis Fimple as Posey
 * John Davis Chandler as Rafe
 * Linda Dano as Rosalie Cutter
 * Slim Pickens as Virgil Cane

Home media
The film was released on DVD by Mill Creek Entertainment on July 5, 2005. It was later released by Dead Of Night on February 20, 2006. It was re-released by Mill Creek on September 12, that same year. In 2015, it was released by Movies Unlimited and Willette Acquisition Corp. on July 10, and 20th respectively.

title: The Shadow of Chikara


text:
Huangjinkou station

Huangjinkou Station, is a station of Line 4 of Wuhan Metro. It entered revenue service on December 28, 2014. It is located in Hanyang District.

title: Huangjinkou station


text:
Talk:David Mirfin

Created Link
Only because I wasn't quite sure of what a "professional foul" is and found it on wiki, I made a link of it. —Preceding unsigned comment added by <IP_ADDRESS> (talk) 05:37, 24 October 2010 (UTC)

External links modified
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title: Talk:David Mirfin


text:
Carnage Gaming Convention

Carnage is a multi-genre table-top gaming convention based in the Upper Valley of Vermont / New Hampshire. It typically covers all genres of tabletop gaming, like board games, role-playing games, CCGs, LARPs and historical and fantasy miniatures.

Carnage was featured on WCAX's The :30 on November 1, 2011.

History
First held in 1998 in West Lebanon, Carnage grew from the motivation "to give New England gamers a place where they could come, be themselves, enjoy their games and have fun." After its inaugural year in New Hampshire, Carnage based itself on the Vermont side of the Upper Valley, moving to Brownsville, VT in 1999 and then to Fairlee in 2003. In 2012, the organizers announced Carnage 2013 would be held at the Killington Grand Hotel. Carnage was once again on the move in 2019 with the organizers deciding to move the convention to the Mt Snow Resort in Dover, Vermont for the 2020 interaction. This move would allow the convention to continue to expand and locate it more centrally in New England. The COVID 19 pandemic postponed the planned move with the 2020 edition of Carnage being held instead as a virtual event; the change in venue will instead occur in 2021 for the 24th year of the convention.

Past conventions

 * Carnage at the Crossroads, November 6–8, 1998, Radisson Inn, West Lebanon, NH
 * Carnage on the Mountain 2, November 5–7, 1999, Ascutney Mountain Resort, Brownsville, VT
 * Carnage on the Mountain 3, November 3–5, 2000, Ascutney Mountain Resort, Brownsville, VT
 * Carnage on the Mountain 4, November 2–4, 2001, Ascutney Mountain Resort, Brownsville, VT
 * Carnage on the Mountain 5, November 1–3, 2002, Ascutney Mountain Resort, Brownsville, VT
 * Carnage by the Lake 6, October 24–26, 2003, Lake Morey Resort, Fairlee, VT
 * Camp Carnage 7, November 5–7, 2004, Lake Morey Resort, Fairlee, VT
 * Carnage 8: Signs Point to Carnage, November 11–13, 2005, Lake Morey Resort, Fairlee, VT
 * Carnage 9 From Outer Space, November 10–12, 2006, Lake Morey Resort, Fairlee, VT
 * Carnage, We’re Hangin’ 10, November 2–4, 2007, Lake Morey Resort, Fairlee, VT
 * This Is Carnage: We Go to 11!, November 7–9, 2008, Lake Morey Resort, Fairlee, VT
 * Carnage 12: Nothing But Carnage, November 6–8, 2009, Lake Morey Resort, Fairlee, VT
 * Carnage the 13th, November 5–7, 2010, Lake Morey Resort, Fairlee, VT
 * Carnage in Wonderland 14: Down the Rabbit Hole, November 4–6, 2011, Lake Morey Resort, Fairlee, VT - Host of 2011 North American Diplomacy Championships (DipCon)
 * Carnage Noir 15, November 2–4, 2012, Lake Morey Resort, Fairlee, VT focused on a film noir/pulp fiction theme.
 * Carnage on the Mountain 16, November 8–10, 2013, Killington Grand Hotel in Killington, Vermont
 * A Fistful of Carnage, November 7–9, 2014, Killington Grand Hotel in Killington, Vermont
 * Carnage in the Lost World, November 6–8, 2015, Killington Grand Hotel in Killington, Vermont
 * Carnage Royale, November 4–6, 2016, Killington Grand Hotel in Killington, Vermont
 * Carnage XX, November 3–5, 2017, Killington Grand Hotel in Killington, Vermont
 * Carnage 21: A Space Odyssey, November 2-4, 2018, Killington Grand Hotel in Killington, Vermont
 * Carnage 22 was held at the Killington Grand Hotel in Killington, Vermont, November 1–3, 2019. The theme for 2019 was an homage to Joseph Heller's novel Catch-22.
 * Carnage 23 was held as a virtual convention due to the COVID 19 pandemic November 7-8, 2020.
 * Carnage 24: Lost in the Carnage Triangle was held at the Mount Snow Resort in Dover, Vermont, November 5-7, 2021.
 * Carnage 25: Silver Jubilee was held at the Mount Snow Resort in Dover, Vermont, November 4-6, 2022.
 * Carnage 26, was held at the Killington Grand Hotel in Killington, Vermont, October 27-29, 2023
 * Carnage 27, will be held at the Killington Grand Hotel in Killington, Vermont, November 1-3, 2024

Previous themes have included: the wild west, horror, B-movie sci-fi, heavy metal (a la Spinal Tap), surf, Alice in Wonderland and summer camp.

Events
Carnage accepts submissions from GMs, or game masters, volunteering to host sessions of games across the tabletop genres. Typical fare includes board games of the Eurogame and Amerigame varieties, collectible card games like Magic: the Gathering and Legend of the 5 Rings, boffer and dialogue-driven LARPs, miniatures in fantastic and historical milieux, and role-playing games, including ongoing campaigns in living worlds and standalone adventures. Recently Carnage has started including learn-to events such as introduction classes and miniature painting and game creation seminars.

Carnage also offers a number of non-gaming events such are "sip'n paints", needle felting and a steam punk fashion show.

Other notable events at Carnage have included the Carnage Accords, an annual Diplomacy tournament; a computer-assisted game trade known as a "math trade"; the Centuries of Conflict umbrella theme for many historical miniatures; dramatic readings and panels held by convention guests; and most recently at Carnage Noir, a geek pub quiz sponsored by Gygax magazine.

In 2022 Carnage is slated to be the host convention for the Diplomacy World Championships (World DipCon).

Guests
Carnage has hosted a number of guests of honor from the gaming industry and literary communities. Past game-related guests have included: James Carpio, Ann Dupuis, Walter Hunt, Tracy Hurley,  Steffan O'Sullivan, Jeff Talanian, Brad Younie, and members of Steve Jackson Games' Men In Black demo team. In 2019 Carnage welcomed David Phipps, creator of Pulp Alley, a skirmish level miniatures game.

Authors have included C. J. Henderson, Howard Coffin and Lisa Comstock.

Artist Don Higgins has made several appearances.

title: Carnage Gaming Convention


text:
Talk:List of butterflies of Madagascar

Missing
Hello,

It seems there is a missing in this list : Where is Chrysiridia rhipheus ?? an endemic butterfly of Madagascar considered one of the most impressive and appealing-looking lepidopterans !! (ref in the article). As you know, the family 	Uraniidae is not too in this list! so strange (mistake!!) This list isn't exhaustive, it must be said in the beginning of the article --Titou (talk) 13:09, 2 July 2016 (UTC)
 * Another = Bunaea aslauga / family Saturniidae! I make the modification to say the following list isn't exhaustive --Titou (talk) 13:32, 2 July 2016 (UTC)

title: Talk:List of butterflies of Madagascar


text:
Filmmaking Basics/Planning the Movie/Audio

 * Lesson
 * WikiU Film School - Lesson #003: Planning the Movie - Audio Considerations

 * Pages of this Lesson
 * Title Page
 * Page 1 - The Animatic
 * Page 2 - Filming
 * Page 3 - Animation
 * Page 4 - Aspect Ratio & Frame Size
 * Page 5 - Audio Considerations → You Are Here!

 * Current Location
 * Wikiversity - English → Faculty for Humanities → The School of Art and Design → The Division of Fine Arts → The Subdivision of Film and Television → The Department of Narrative Film Production →  WikiU Film School:Course: WikiU Film School Course 01 - Learning the Basics of Filmmaking  →  Lesson #003: Planning the Movie →  Page 5 - Audio Considerations

Audio Considerations
Audio CD quality is very easy to work with. DV requires higher quality audio. Which will we work with?

to be completed shortly Robert Elliott 03:37, 30 September 2006 (UTC)


text:
cappotto

Etymology 1
From.

Noun

 * 1)  coat, overcoat
 * 2)  greatcoat
 * 3)  whitewash complete victory or series of victories without suffering any losses; a clean sweep

title: cappotto


text:
Balford Farms

Balford Farms is an American dairy company located in Burlington, New Jersey. It is the oldest privately-owned and operated independent distributor in the Lehigh Valley region.

History
Balford Farms was founded in 1892 by a teenager named Frank B. Baldwin, using a horse and wagon to deliver milk to customers throughout Philadelphia, Pennsylvania after school.

In 1965, the company, then called Baldwin Dairies, merged with Frankford Dairies of Philadelphia to become Baldwin-Frankford Dairies, Inc. George H. Baldwin, Sr. and John Baldwin, grandsons of Frank B. Baldwin, changed the name to Balford Farms in 1972.

Expansion of Balford continued in 1980 with the purchase of a 70,000 ft2 (6,503 m2) warehouse in Bensalem, Pennsylvania. Over the next few years, the company acquired small independent dairy and food companies to become a major distributor in the Lehigh Valley. Balford Farms merged with another longtime business in Philadelphia, Quality Dairy Products (operating as Breuninger's Dairy) in 1996.

Dairy Farmers of America sold their warehousing and distribution center in Harleysville, Pennsylvania to Balford in 2012, formerly owned by Keller's Creamery, as part of a consolidation project.

The company also acquired Rosenberger's Dairy of Hatfield, Pennsylvania.

title: Balford Farms


text:
avô

Etymology
From, from , ultimately from , from.

Noun

 * 1) grandfather, male grandparent

Usage notes
Avô has two plural forms, avôs and avós. The former (os avôs) means exclusively a group of two or more men (cf. English grandfathers), the latter (os avós) is used for a group of both men and women (cf. English grandparents). Both are masculine nouns. The plural of avó (grandmother) is a regular feminine noun (as avós) and means grandmothers. This is one of the few Portuguese nouns that have a tripartite plural inflection, the others being, , , and other derived terms.

title: avô


text:
konjugoida

Etymology
(see 🇨🇬), ultimately from and adapted with the verbal suffix.

Verb

 * 1) To conjugate.

title: konjugoida


text:
prosessoida

Etymology
(see 🇨🇬), ultimately from and adapted with the verbal suffix.

Verb

 * 1)  To process an industrial product.

title: prosessoida


text:
Yakiv Medvetskyi

Very Reverend Yakiv Medvetskyi (Яків Медвецький; Jakub Medwecki; 7 January 1880 in Tsvitova, Austro-Hungarian Empire /present day in Chortkiv Raion, Ternopil Oblast, Ukraine/ – 27 January 1941 in Kraków, General Government /present day in Poland/) was a Greek Catholic hierarch. He served as the second Apostolic Administrator of the Apostolic Administration of Lemkowszczyzna from 3 July 1936 until his death on 27 January 1941.

Life
Yakiv Medvetskyi was born in the family of Greek-Catholics in 1880 in the Ukrainian Catholic Archeparchy of Lviv. After graduation of the popular school and gymnasium education in Buchach and Stanislaviv, he joined the Greek-Catholic Theological Seminary in Lviv (1900–1904).

He was ordained as priest on 7 April 1905 by Bishop Blessed Hryhoriy Khomyshyn for the Eparchy of Stanislaviv, after completed his studies. After the one year parish work, Fr. Medvetskyi continued to study in the University of Vienna with Doctor of Theology degree in 1910. He was a professor of the Biblical subjects in the Theological Seminary in Stanislaviv from 1910 until 1936 and vice-rector of the same Seminary from 1912 until 1936.

On 3 July 1936 Fr. Medvetskyi was appointed by Pope Pius XI the second Apostolic Administrator of the Apostolic Administration of Lemkowszczyzna (that later was elevated in the rank of Apostolic Exarchate) without dignity of bishop.

Apostolic Administrator Medvetskyi suffered from diabetes mellitus. He died in a hospital in Kraków, due to complications after surgery on 27 January 1941 at the age 61.

title: Yakiv Medvetskyi


text:
Talk:David Troughton

Wellington at Sharpe's
Why was he replaced by Hugh Fraser? Well both did a good role but why?--<IP_ADDRESS> (talk) 00:19, 24 January 2011 (UTC)

Mother's name?
According to this article, his mother's name was Margaret Dunlop. But according to this [] his father's wife's name was Sheila Dunlop. I realize that it is possible that he married two women both called Dunlop, but I'd welcome confirmation. <IP_ADDRESS> (talk) 18:13, 28 November 2014 (UTC)

External links modified
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External links modified
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I have just modified one external link on David Troughton. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20161130185440/https://www.rsc.org.uk/king-lear/cast-and-creatives to https://www.rsc.org.uk/king-lear/cast-and-creatives

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Jewish?
I don't know where they get the idea from that he might be Jewish. I see no mention of this in his father's article. His mother's maiden name was Dunlop, a Scottish name from Ayrshire, doesn't sound Jewish. His father's second partner was called Nuens, might just possibly be a Jewish name. PatGallacher (talk) 01:33, 26 February 2024 (UTC)

title: Talk:David Troughton


text:
Category:Discoveries by Heinrich Louis d'Arrest

This is a category for astronomical objects discovered by German astronomer Heinrich d'Arrest.

See parent category for proper sortkey usage instructions.


text:
Semyonov's Rebellion

Semyonov's Rebellion refers to the 1917 revolt led by Captain G. M. Semyonov of the Kazak Army, against Soviet control, within the Eastern Region (lit. Further-Baikal Region) of Russia. It is part of the White Movement, and the Russian Civil War (lit. Civil War in the Far East).

In June 1917, G. M. Semyonov was commissioned by the Russian War Commission to form a standing army, composed of Kazak, Mongol, and Buryat horseback forces. However, his work was interrupted by the regime change following the October Revolution.

Following the October Revolution, and after receiving further authorization from the Petrograd Council of Work and Soldier Deputies, Semyonov continued assembling his troops. Contrary to his orders he accepted Russians into his ranks, conditional upon their denunciation of "revolutionism".

As word reached the Petrograd Council that Semyonov was assembling Anti-Revolutionary forces they withheld money promised for the compensation of his army.

On 18 November 1917, Semyonov began an anti-Soviet revolt, seizing control of the lower Berezovka train station. Then, attending a city council in nearby Verkhneudinsk (now Ulan-Ude), he called citizens to overturn the local government and engage in a "merciless war against Bolshivism". The council responded by authorizing the police force (lit. "General Safety Commission") and forces of the oblast council to arrest Captain Semyonov and disarm his regiment. Semyonov resisted by force, in turn traveling to Chita where he arrested Pumpyansky, the head of the Chitian Ruling Council. He also appropriated funds for his army before fleeing to Manzhouli. With support from other local forces, and General D. L. Horvata, the managing officer of the Chinese-East Railroad (China East Iron Road, or "КВЖД") Semyonov formed the Manzhouli Standing Army, composed of around 500 men on horseback. They continued to raid railway stations and incite rebellion.

Eventually the Soviet Army was forced to dispatch a large military force to restore control in the region. These forces were led by Sergei Lazo, from the Central Siberian Council. Their battles with Semyonov's army constituted one of the first fronts of the Civil War in the Far East. Semyonov was considered a candidate for assistance from several foreign governments with interests running counter to the USSR, including the United States. Although Semyonov received support from the Japanese and was initially successful at holding the city of Chita, his forces did eventually suffer defeat around April 1918.

The Remainder of Semeyonov's Military Career
Semeyonov was active in anti-soviet operations until September 1921. When he was unable to remain in Russia, Semyonov moved to the United States for a time, although he was accused of committing acts of violence against the American soldiers of the Expeditionary Corps. He was eventually acquitted and returned to China, where he received a monthly 1000-yen pension by the Japanese government. In Tianjin he made ties with the Japanese intelligence community and mobilized exiled Russian and Cossack communities, planning to eventually overthrow the Soviets. He was also employed by Puyi, the dethroned Emperor of China, whom he wished to restore to power.

Semyonov was captured in Dalian by Soviet paratroopers in September 1945 during the Soviet invasion of Manchuria. He was charged with counterrevolutionary activities and sentenced to death by hanging by the Military Collegium of the Supreme Court of the USSR. He was executed on August 29, 1946.

title: Semyonov's Rebellion