We perform variable separation in the quasi-potential systems of equations of
the form q¨=−A−1∇k=−A~−1∇k~{}, where A
and 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.Comment: LaTex, 30 pages, to appear in J. Phys. A: Math. Ge