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Integration of a generalized Hénon-Heiles Hamiltonian

C. Verhoeven·M. Musette·R. Conte
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Abstract

The generalized Hénon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $μY^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.

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C. Verhoeven, M. Musette, R. Conte. 2001-12-19. Integration of a generalized Hénon-Heiles Hamiltonian. https://doi.org/10.1063/1.1456948

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