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I seem to recall reading in
mechanics books that only the inverse square and harmonic oscillator force laws give rise to
closed orbits.
But how does one prove in general that orbits are closed in a given problem?
Suppose either you
are given differential equations for r(t) and phi(t), which one should probably be able to
translate into a second-order equation for r(phi), or equivalently say you are given the force
expression and relevant conservation laws?