Classical Dynamics of Particles and Systems · Problem 11-27

Coupled Oscillations — Marion & Thornton

Physics — Mechanics · symmetric-body-force-free-precession

Problem

A symmetric body moves without the influence of forces or torques. Let

x_3

be the symmetry axis of the body and

\mathbf{L}

be along

x_3'

. The angle between

\boldsymbol{\omega}

and

x_3

\alpha

. Let

\boldsymbol{\omega}

and

\mathbf{L}

initially be in the

x_2

x_3

plane. What is the angular velocity of the symmetry axis about

\mathbf{L}

in terms of

I_1

I_3

\omega

, and

\alpha