Show that if the potential in the Lagrangian contains velocity-dependent terms, the canonical momentum corresponding to a coordinate of rotation θ of the entire system is no longer the mechanical angular momentum Lθ but is given by pθ = Lθ − i n ? ri 3∇viU, where ∇v is the gradient operator in which the derivatives are with respect to the velocity components and n is a unit vector in the direction of rotation. If the forces are electromagnetic in character, the canonical momentum is therefore pθ = Lθ + i n ? ri 3 qi c Ai .