INTEGRABILITY, STACKEL SPACES, AND RATIONAL POTENTIALS

For a variety of classical mechanical systems embeddable into flat spa ce with Cartesian coordinates {x(i)} and for which the Hamilton-Jacobi equation can be solved via separation of variables in a particular cu rvalinear system {u(j)}, we answer the following question. When is the separable potential function upsilon expressible as a polynomial (or as a rational function) in the defining coordinates {x(i)}? Many examp les are given. (C) 1997 American Institute of Physics.