Classical Dynamics of Particles and Systems · Problem 1-26

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · plane-polar-coordinates

Problem

A particle moves with

v = \text{const.}

along the curve

r = k(1 + \cos\theta)

(a cardioid). Find

\ddot{r} \cdot \mathbf{e}_r = \mathbf{a} \cdot \mathbf{e}_r

|\mathbf{a}|

, and

\dot{\theta}