Pairs of commuting Hamiltonians quadratic in the momenta
Abstract
In the case of two degrees of freedom, we consider pairs of Hamiltonians quadratic in the momenta and commuting with respect to the standard Poisson bracket. We find new multiparameter families of such pairs and present a universal scheme for constructing a complete solution of the HamiltonJacobi equation in terms of integrals over an algebraic curve. For the most complicated examples, this curve is a nonhyperelliptic covering of an elliptic curve.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 November 2006
 DOI:
 10.1007/s112320060129y
 Bibcode:
 2006TMP...149.1425M
 Keywords:

 integrable Hamiltonian system;
 separation of variables;
 algebraic system