Integrability, Stäckel spaces, and rational potentials

E. G. Kalnins; S. Benenti; Willard Miller

doi:10.1063/1.531977

Integrability, Stäckel spaces, and rational potentials

E. G. Kalnins, S. Benenti, Willard Miller

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Abstract

For a variety of classical mechanical systems embeddable into flat space with Cartesian coordinates {x_i} and for which the Hamilton-Jacobi equation can be solved via separation of variables in a particular curvalinear system {u_j}, we answer the following question. When is the separable potential function υ expressible as a polynomial (or as a rational function) in the defining coordinates {x_i}? Many examples are given.

Original language	English (US)
Pages (from-to)	2345-2365
Number of pages	21
Journal	Journal of Mathematical Physics
Volume	38
Issue number	5
DOIs	https://doi.org/10.1063/1.531977
State	Published - May 1997
Externally published	Yes

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Integrability, Stäckel spaces, and rational potentials

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