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 υ expressible as a polynomial (or as a rational function) in the defining coordinates {xi}? Many examples are given.
Original language | English (US) |
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Pages (from-to) | 2345-2365 |
Number of pages | 21 |
Journal | Journal of Mathematical Physics |
Volume | 38 |
Issue number | 5 |
DOIs | |
State | Published - May 1997 |
Externally published | Yes |