In Example 13.3 (page 531) we saw that if we write the

QUESTION:

In Example 13.3 (page 531) we saw that if we write the Hamiltonian for a two-dimensional central force problem in terms of polar coordinates r and 0, then the coordinate 0 is ignorable. Write down the Hamiltonian for the same problem, but using rectangular coordinates x, y. Show that, with this choice, neither coordinate is ignorable. [The moral of this is that the choice of generalized coordinates calls for some care. In particular, you must look for any symmetries in a system and try to choose generalized coordinates to take advantage of them.]