A particle of mass m slides without friction on a wedge of angle a and mass M that can move without friction on a smooth horizontal surface. Treating the constraint of the motion on the wedge by the method of Lagrange multipliers, find the equations of motion for the particle and wedge. Also, obtain an expression for the forces of constraints. Calculate the work done in time t by the forces of constraint acting on the particle and on the wedge. What are the constants of motion for the system?