TITLE: "You can't push a rope"
QUESTION [11 upvotes]: "You can't push a rope" is a wisdom saying that some engineering teachers pass along to their students.  Since I'm not an engineer, I can only guess at what they mean, but it sounds to me like code for a mathematical principle (but from control theory? numerical analysis? ergodic theory? dynamical systems? statistics?)
1) I would appreciate having any mathematicians who work with engineers hazard a general framework for a rigorous formulation of what the engineers mean by this slogan.
2) I would like to know of any deep theorems that (of the no-go variety) that naturally fall under this rubric (whether engineers know about these theorems or not).

REPLY [10 votes]: The rigorous mathematical context is stability. A straight rope in either tension or compression is a valid solution of the underlying PDE, but in compression this solution is unstable, so it cannot be realized in practice.