Question

A solid homogeneous cylinder of radius 'a' rolls without slipping inside a stationary hollow cylinder of large radius R. Write the Lagrangian and show that the motion of solid cylinder is simple harmonic.

Answer 1

\[
T = \frac{1}{2} m (\dot r^2 +r^2 \dot \theta^2 + r^2 \sin^2\theta \dot \phi^2) \\
V = mg(r + r\cos \theta) \]