Wheels within Wheels: Hamiltonian Dynamics as a Hierarchy of Action Variables
In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate. This result is then used to demonstrate that the action integral acts as a Hamiltonian for slow coordinates providing time is scaled to the "tick time" of the oscillating coordinate. Numerous examples, including charged particle drifts and relativistic motion, are supplied to illustrate the varied application of these results.
© 2010 American Physical Society. Received 28 April 2010; published 14 September 2010. Supported by U.S. DOE and NSF.
Published - Perkins2010p11539Phys_Rev_Lett.pdf
Accepted Version - 1008.1379.pdf