1. An object of mass m is moving without friction on the inner surface of a sphere of radius R. gravity The acceleration is. Using a spherical coordinate system (1.0.0) with the center of the sphere as the origin, (a) Find the Lagrangian L(0,0,0,0), and write the equations of motion for 8(t) and (t). (b) Find the two conserved quantities by analyzing the body's equation of motion, and obtain them as a function of the initial (c) In order for this object to satisfy the constraint of = R and move on the spherical surface, it must receive (d) Among the initial conditions, 66=x/2 and =0. In order for an object to rise to the highest point without falling off the surface of the sphere, > must be present. Find