Integrable one-particle potentials related to the Neumann system and the Jacobi problem of geodesic motion on an ellipsoid

Abstract

There are found here two families of elementary one-particle potentials of n degrees of freedom which are separable in elliptical-spherical coordinates or in generalized elliptic coordinates. The first family is also integrable if the particle is moving on an n-dimensional sphere. The second family remains integrable when a particle is constrained to the n-axial ellipsoid.