A uniform solid cylinder C with mass m and radius a rolls on the rough outer surface of a fixed horizontal cylinder of radius b. In the motion, the axes of the two cylinders remain parallel to each other. Let θ be the angle between the plane containing the cylinder axes and the upward vertical. Taking θ as generalised coordinate, obtain Lagrange's equation and verify that it is equivalent to the energy conservation equation.
Initially the cylinder C is at rest on top of the fixed cylinder when it is given a very small disturbance. Find, as a function of θ, the normal component of the reaction force exerted on C. Deduce that C will leave the fixed cylinder when θ=cos−1(4/7). Is the assumption that rolling persists up to this moment realistic?