Is central motion stable with criteria for force function f(r)?

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SUMMARY

In central motion, stability is determined by the criteria involving the force function f(r), specifically when f'(r) + 3/r > 0. This condition ensures that small perturbations to the satellite's orbit do not result in escape but rather cause oscillations in the radial direction while maintaining the orbit. The discussion also touches on the relationship between this stability and the calculations of the Lyapunov exponent, indicating that periodic orbits can exist under these stability conditions.

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LagrangeEuler
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In central motion we have criteria for stability. For function of force f(r)
we have stability if
f'(r)+\frac{3}{r}>0

This is stability in what sence? Do I have then periodic orbits or what? Is it in some connection with calculations of Lyapunov exponent? Thanks for the answer.
 
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Stability in the sense that if you give the satellite a little push, it doesn't escape the orbit, rather it oscillates in the radial direction, while orbiting!(Just imagine a sinusoid with a circle as the x axis!)
 

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