Q.4 Consider a coin rolling without slipping across a horizontal plane such that the plane of the coin remains vertical, but it is free to rotate about the vertical axis. Find out the generalized coordinates required to describe the motion. Write the rolling constraint in differential form Is that constraint equation integrable? Is the constraint holonomic? Q.5 Find the equation of constraint for a sphere of radius a constained to roll without slipping on the lower half of the inner surface of the hollow cylinder of inside radius R. Q.6 A particle moves in the xy-plane under the constraint that its velocity vector is always directed towards a point on the x-axis whose abscissa is some given function of time f(t). Show that for f(t) differentiable, but otherwise arbitrary, the constraint is non-holonomic.