Is it necessary to attain stability to have equilibrium?

Question

Is it necessary to attain stability to have equilibrium?

Answer 1

It maybe the other way around: it is necessary to obtain equilibrium to have stability. Equilibrium is the state, while stability is the measure.

Hope this helps.

Answer 2

No, for example a pendulum has two equilibrium points, one when it is facing down, and one when it is facing up. The former is stable because a small change in the position will eventually be in the same equilibrium, the latter is not stable because a small change in the position of the pendulum will not lead to the same equilibrium.

Answer 3

Answer is no.

Imagine those circus performers standing still on a ball.

Are they stable? No. A slight move they can fall from their position.

Are they in equilibrium? Yes since they are at rest.

Stability is how easy you can get back to your original position when disturbed. The easier you can restore to your original position, the more stable you are.  

Answer 4

No, for example a spherical object at rest on a flat table is in equilibrium but it is not stable; that is to say it will not return to its initial position when subjected to an arbitrarily small perturbation.