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

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.

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

References in corpus (1)

• From bi-Hamiltonian geometry to separation of variables: stationary Harry-Dym and the KdV dressing chain

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• Bi-Hamiltonian representation of Stäckel systems
• Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems
• Presymplectic representation of bi-Hamiltonian chain
• Non-Hamiltonian systems separable by Hamilton-Jacobi method
• A class of Poisson-Nijenhuis structures on a tangent bundle
• Separability preserving Dirac reductions of Poisson pencils on Riemannian manifolds