Classical Mechanics (Kibble & Berkshire) · Problem 7.5

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

Physics — Mechanics · path-equation

Problem

A particle

P

moves under the attractive inverse square field

\boldsymbol{F} = -(m\gamma/r^2)\hat{\boldsymbol{r}}

. Initially

P

is at the point

C

, a distance

c

from

O

, and is projected with speed

(3\gamma/c)^{1/2}

perpendicular to

OC

. Find the polar equation of the path and make a sketch of it. Deduce the angle between

OC

and the final direction of departure of

P