Energy, Angular Momentum, and Stable Equilibrium
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Write down the equations of motion in polar coordinates for a particle of unit mass moving in a plane under a force with potential energy function V = -k ln r + cr + gr cos (theta), where K, c and g are positive constants. Find the positions or equilibrium (a) if c > g, and (b) if c < g. By considering the equations of motions near these points, determine whether the equilibrium is stable (i.e. will the particle, if given a small displacement, tend to return repeatedly?
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This solution provides calculations to determine whether an equilibrium is stable.
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