Geodesic
Pairs of commuting Hamiltonians quadratic in the momenta
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 147-160 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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V. G. Marikhin; V. V. Sokolov. Pairs of commuting Hamiltonians quadratic in the momenta. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 147-160. http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a0/

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