Apply the lagrangian method with spherical polar coordinates, for a particle moving in a central force described by a potential energy U(r). (Use the physicists notation, for which the relations between cartesian and spherical coordinates are x = r sinθ cosφ , y = r sinθ sinφ , z = r cosθ .)
a) Write down the lagrangian in spherical coordinates, and generate the three differential equations of motion.
b) Which, if any, of the three generalised momenta are conserved for a central force?