TITLE: Why is a dynamical system not a dynamic system?
QUESTION [12 upvotes]: This is a research question in the history of math, I suppose.
As a non-native english speaker I became used to mathematical expressions like 'dynamical' and 'tangential'. When using them in daily conversation as substitutes for 'dynamic' and 'tangent' I got frowned upon by native english speakers who claimed to have never heard of these words before.
Some references suggest
https://www.merriam-webster.com/dictionary/dynamical
https://www.merriam-webster.com/dictionary/tangential
that indeed they can almost mean the same as 'dynamic' and 'tangent' but for some reason nobody seems to use these words that way.
So whereas in English:
A dynamic person-a dynamical system
the adjective is different
it is in French
une personne dynamique- un système dynamique
and in German
Eine dynamische Person - ein dynamisches System
the adjective is the same.
I am wondering when (and maybe also why) these expressions started deviating in English.

REPLY [11 votes]: Thing is, they do not mean the same thing. At least, not in theory.
Dynamic the adjective means "exhibiting continual change".
Dynamics the noun means "the study of forces and their relation to motion".
Dynamical the adjective means "relating to the study of dynamics."
A "dynamic" system is a system exhibiting continual change. A "dynamical" system is a system relating to the study of dynamics. (Since OP is Chinese, this is also why DS is 動力系統 and not 不定系統.)
Similarly,
Tangent the adjective means the geometric notion of touching but not intersecting.
Tangent the noun refers first to the geometric construct of the line tangent to a shape, and then also to the idea of "objects that can be split off without making a turn", whence the idea of "going on a tangent" when you derail the discussion with something related but not directly relevant. (You won't be going on a tangent if you change the topic or the direction of discussion abruptly.)
Tangential the adjective refers to the quality of "tangent". Hence you make a "tangential remark" while you "go on a tangent". Hence you look for "tangent lines" while compute "tangential forces". (The force itself is not tangent, but it is directly along the line that is tangent to the object.)

This, of course, gets muddled by the fact that English is perfectly happy with attributive nouns. English being remarkably loosey goosey about grammar for a Western language, understanding in theory why things are the way they are is probably much less useful than accepting their use as a convention. (After all, what is language but a convention to enable communication?)

Homework exercise: discuss transverse versus transversal