2. In class we found the Lagrangian for a mass m sliding down, without friction, an inclined plane, which itself can move. The inclined plane has an angle a, slides without friction on a horizontal surface, and has a mass M. We will assume the height of the inclined plane is h, and that the vertical side of the inclined plane is the side closest to the origin and is a distance > > 0 from the origin. The distance along the plane of the mass from the top of the inclined plane is s, so our generalized coordinates are s and x. The Lagrangian is L = =(M + m)x2+ mascosat Ims2 - mg(h - ssina). (a) Find the momenta, Ps and Pr, corresponding to s and x, respectively. (b) We want to find the Hamiltonian for this system. First find it as a function of x, s, x, and s, that is, find H(x, s, x, s). Now a Hamiltonian should be expressed as a function of x, s, Px and Ps. The first step is to find x and s in terms of Px and Ps. Do this. You are now finished with this part of the problem. For the next part of the problem you would have to substitute the expressions you found for a and s in terms of Pr and Psinto H(x, s, x, s) to find H(x, S, PI, Ps)- Do NOT do this. It is messy, and I did it for you. The answer is (you do NOT have to derive this) M +m H(x, S, Px, Ps) = M + msina Px - PIPs Cos at 2m Ps tmg(h-ssina). (c) Using the above equation, find the Hamiltonian equations of motion