Solution (source code)

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= Solution

For $r_0\gg L$, $\Omega/\omega_0\to2$. The potential approaches the isotropic harmonic-oscillator form $kr^2/2$, and the perturbed path is approximately a small-eccentricity ellipse centered on the fixed point. The radius has two maxima and two minima per revolution. For finite nonzero $L/r_0$, the ellipse is an approximation and slow precession can remain.

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