Classical Dynamics of Particles and Systems · Problem 8-15

Dynamics of a System of Particles — Marion & Thornton

Physics — Mechanics · central-force-hyperbolic-cotangent-orbit

Problem

A particle of unit mass moves from infinity along a straight line that, if continued, would allow it to pass a distance

b\sqrt{2}

from a point

P

. If the particle is attracted toward

P

with a force varying as

k/r^5

, and if the angular momentum about the point

P

\sqrt{k}/b

, show that the trajectory is given by

r = b\coth(\theta/\sqrt{2})