A dumbbell is composed of two particles, each of mass m, connected by a massless rod of length l. One particle of the dumbbell is connected by a pivot to the edge of a disk of radius r, which is massless except for a particle of mass m at its center. The disk can roll without slipping on a horizontal surface, and all motion occurs in the vertical plane of the disk. Assuming that θ and Ø are the absolute rotation angles of the disk and dumbbell, as shown, obtain the differential equations of motion. Use Lagrange Eqn.

A dumbbell is composed of two particles, each of mass m, connected by a massless rod of length l. One particle of the dumbbell is connected by a pivot to the edge of a disk of radius r, which is massless except for a particle of mass m at its center. The disk can roll without slipping on a horizontal surface, and all motion occurs in the vertical plane of the disk. Assuming that θ and Ø are the absolute rotation angles of the disk and dumbbell, as shown, obtain the differential equations of motion. Use Lagrange Eqn.