Classical Dynamics of Particles and Systems · Problem 8-31

Dynamics of a System of Particles — Marion & Thornton

Physics — Mechanics · central-force-stable-circular-orbit-force-law

Problem

Consider a force law of the form

F(r) = -\frac{k}{r^2} - \frac{k'}{r^4}

Show that if

\rho^2 k > k'

, then a particle can move in a stable circular orbit at

r = \rho