Separation coordinates in Hénon-Heiles systems. (English) Zbl 1477.85003
Summary: In this paper we apply the method of the Kowalewski’s Conditions to separate the seven Hénon-Heiles integrable systems. For each of them we provide explicitly the separation coordinates in the form of eigenvalues of a matrix \(M\) called Control Matrix. A couple of systems (HH3 KK and HH4 1:12:16) are presented and discussed in a more general form than usually in the literature. We show that the process of separation of coordinates can be reduced, at the end, to the choice of a single function and, eventually, a vector field transversal to the Lagrangian foliation in an extended phase space.
MSC:
| 85A05 | Galactic and stellar dynamics |
| 70H06 | Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics |
| 53D22 | Canonical transformations in symplectic and contact geometry |
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