A system of n particles moves in a plane under the influence of interaction forces derived from potential terms depending only upon the scalar distances between particles.
(a) Using plane polar coordinates for each particle (relative to a common origin), identify the form of the Hamiltonian for the system.
(b) Find a generating function for the canonical transformation that corresponds to a transformation to coordinates rotating in the plane counterclockwise with a uniform angular rate ω (the same for all particles). What are the transformation equations for the momenta?
(c) What is the new Hamiltonian? What physical significance can you give to the difference between the old and the new Hamiltonians?
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