An inverted pendulum on a rolling disk is shown below. The disk has a radius R and mass M and is rolling on a at surface without slipping. The inverted pendulum consists of a rod of length L and mass m. A point mass m is attached to the end of the rod. The inverted pendulum is free to rotate about point 0 of the disk. Note that there is an external force F acting on the center point of the disk, and it is also attached to a dashpot which produces a dampening force proportional to the velocity by a constant C. Also note that gravity acts. Derive the equations of motion for the system using the Lagrange method. //'///'// x//'/'/.//'/'//'/'//'/'//