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This is a partial answer that may get you thinking in the right direction. Three rods connected in a triangle are rigid. 4 our more rods connected in a square or larger polygon are flexible. This is why high voltage power lines are supported by structures built entirely of triangles. However, triangles are not enough to ensure stability. E.G. Two ...


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In the dynamical systems jargon, this is the usual Lyapunov stability. If additionally the system reaches the equilibrium state, then the equilibrium is called asymptotically stable. For the formal definition, see this link: http://www.scholarpedia.org/article/Stability#Definitions:_Stability_of_an_Equilibrium It is also worth to remark that a equilibrium ...


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If there is oscillation, the equilibrium is stable in at least one dimension. The situation where momentum keeps increasing could apply to a driven mass oscillating about a stable equilibrium. It would also apply to a non-driven mass at a saddle point. Consider that the mass begins oscillating approximately, but not exactly, along the concave up curve in ...


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I am not sure of what you mean but in mechanic it's called unstable equilibrium. Check this http://en.wikipedia.org/wiki/Mechanical_equilibrium to get illustration on differents equilibrium states



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