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 Hamilton–Jacobi
equation in terms of integrals over an algebraic curve. For the most
complicated examples, this curve is a nonhyperelliptic covering of an elliptic curve.
Keywords:integrable Hamiltonian system, separation of variables, algebraic system.
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