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

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

2002-01-29

arxiv.org/abs/nlin/0201058v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTex, 30 pages, to appear in J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/35/12/316

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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