Classical Mechanics (Kibble & Berkshire) · Problem 7.1

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

Physics — Mechanics · radial-motion-equation-apses

Problem

A particle

P

of mass

m

moves under the repulsive inverse cube field

\boldsymbol{F} = (m\gamma/r^3)\hat{\boldsymbol{r}}

. Initially

P

is at a great distance from

O

and is moving with speed

V

towards

O

along a straight line whose perpendicular distance from

O

p

. Find the equation satisfied by the apsidal distances. What is the distance of closest approach of

P

O