Integrability, Stäckel spaces, and rational potentials
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Copyright 1997 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jsp
Abstract
For a variety of classical mechanical systems embeddable into flat space with Cartesian coordinates {xi} and for which the Hamilton–Jacobi equation can be solved via separation of variables in a particular curvalinear system {uj}, we answer the following question. When is the separable potential function v expressible as a polynomial (or as a rational function) in the defining coordinates {xi}? Many examples are given.
Citation
Kalnins, E.G., Benenti, S. & Miller, W., Jr. (1997). Integrability, Stäckel spaces, and rational potentials . Journal of Mathematical Physics, 38, 2345.