A thin half-cylindri- E cal shell of weight W = mg rolls without sliding on a flat surface (Fig. ). Derive the equation of motion

Question

A thin half-cylindrical shell of weight W = mg rolls without sliding on a flat surface (Fig. ). Derive the equation of motion using the Lagrange formalism.

Answer 1

The system is ****; it has one degree of freedom. We introduce the coordinate ϕ as shown in the figure. With the distance a = 2r/π of the center of mass C from the center M of the shell we have

Thus, the potential energy V , the kinetic energy T , the Lagrangian and the pertinent derivatives are

Introduction into

yields the equation of motion: