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Separation of variables in quasi-potential systems of bi-cofactor form

Krzysztof Marciniak·Maciej Blaszak
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Abstract

We perform variable separation in the quasi-potential systems of equations of the form $\ddot{q}=-A^{-1}\nabla k=-\tilde{A}^{-1}\nabla\tilde{k}${}, where $A$ and $\tilde{A}$ are Killing tensors, by embedding these systems into a bi-Hamiltonian chain and by calculating the corresponding Darboux-Nijenhuis coordinates on the symplectic leaves of one of the Hamiltonian structures of the system. We also present examples of the corresponding separation coordinates in two and three dimensions.

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Krzysztof Marciniak, Maciej Blaszak. 2002-01-29. Separation of variables in quasi-potential systems of bi-cofactor form. https://doi.org/10.1088/0305-4470%2F35%2F12%2F316

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