Determination of separation coordinates for potential and quasi-potential Newton systems

Abstract: When solving Newton systems q = M(q), q ϵ Rn, by the method of separation of variables, one has to determine coordinates in which the related Hamilton-Jacobi equation separates.The problem of finding separation coordinates for potential Newton systems q = -∇V (q) goes back ta Jacobi. In the first part of this thesis we give a complete solution to this classical problem. It can also be used to find separation coordinates for the Schrödinger equation.In the second part of this thesis, we study separability for quasi-potential systems q = -A(q)-1∇W(q) of generic cofactor pair type. We define separation coordinates that give these systems separable Stäckel form. The two most important families of these coordinates (cofactor-elliptic and cofactor-parabolic) generalize the Jacobi elliptic coordinates, and are shown to be defines by elegant rational equations.