Classical Dynamics of Particles and Systems · Problem 11-25
Coupled Oscillations — Marion & Thornton
Physics — Mechanics · disk-two-halves-lagrangian
Problem
Consider a thin disk composed of two homogeneous halves connected along a diameter of the disk. If one half has density ρ and the other has density 2ρ, find the expression for the Lagrangian when the disk rolls without slipping along a horizontal surface. (The rotation takes place in the plane of the disk.)