Introduction to Classical Mechanics · Problem 3.69

Oscillations — Morin

Physics — Mechanics · polar-coordinates-force

Problem

A force

F_\theta = 2m\dot{r}\dot{\theta}

** Consider a particle that feels an angular force only, of the form

F_\theta = 2m\dot{r}\dot{\theta}

. Show that

r = Ae^\theta + Be^{-\theta}

, where

A

and

B

are constants of integration, determined by the initial conditions. (This force is actually a physical one. If you put a bead on a stick and swing the stick around one end at a constant rate, then the normal force from the stick happens to be

2m\dot{r}\dot{\theta}

Related theory

Polar Coordinates

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