A uniform rod of length L and mass M is pivoted at O and can swing in a vertical plane (Fig. P12.13). The other end of the rod is pivoted to the center of a thin disk of mass M and radius R. (The rod swings, while the disk swings as well as rotates.) Using Lagrange's equations, derive the equations of motion for the system and describe the motion.

A uniform rod of length L and mass M is pivoted at O and can swing in a vertical plane (Fig. P12.13). The other end of the rod is pivoted to the center of a thin disk of mass M and radius R. (The rod swings, while the disk swings as well as rotates.) Using Lagrange's equations, derive the equations of motion for the system and describe the motion.