Eisenhart lift for Euler’s problem of two fixed centers

摘要

We apply the approach of Eisenhart lift to the classical Euler’s bicentric system, yielding a three-dimensional geodesic system. An extra potential is added to the geodesic Hamiltonian to preserve the separability of the system. We also make a generalization of the system by Jacobi method. The Stäckel separability of all of these systems are verified. Their Hamilton–Jacobi equations are integrated in principle. The explicit forms of the Killing tensors on the associated Riemannian manifolds are also shown.