Classical Dynamics of Particles and Systems · Problem 2-40

Oscillations — Marion & Thornton

Physics — Mechanics · two-dimensional-orbit-acceleration

Problem

A particle moves in a two-dimensional orbit defined by

x(t) = A(2\alpha t - \sin\alpha t)

y(t) = A(1 - \cos\alpha t)

(a) Find the tangential acceleration

a_t

and normal acceleration

a_n

as a function of time where the tangential and normal components are taken with respect to the velocity. (b) Determine at what times in the orbit

a_n

has a maximum.