(a) The point of suspension of a plane simple pendulum of mass m and length l is constrain...

(a) The point of suspension of a plane simple pendulum of mass m and length l is constrained to move along a horizontal track and is connected to a point on the circumference of a uniform flywheel of mass M and radius a through a mass- less connecting rod also of length a, as shown in the figure. The flywheel rotates about a center fixed on the track. Find a Hamiltonian for the combined system and determine Hamilton’s equations of motion.

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(b) Suppose the point of suspension were moved along the track according to some function of time x = f(t), where x reverses at x = ±2a (relative to the center of the fly wheel). Again, find a Hamiltonian and Hamilton’s equations of motion.