Classical Mechanics (Kibble & Berkshire) · Problem 7.21

Non-linear oscillations and phase space — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · assorted-inverse-square-problems

Problem

A body moving in an inverse square attractive field traverses an elliptical orbit with eccentricity ee and major axis 2a2a. Show that the time average of the distance rr of the body from the centre of force is a(1+12e2)a(1 + \tfrac{1}{2}e^2). [Transform the time integral to an integral with respect to the eccentric angle ψ\psi.]

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