An Analysis of the Restricted Euler Problem Using Symplectic Integrators

Abstract

The Three-Body Problem is far from fully solved despite centuries of effort. The restricted Euler Problem is a special case in which two bodies are fixed in place, resulting in two Poisson-commuting conserved quantities, allowing the system to be fully integrable by the Liouville-Arnold theorem. We analysed the restricted Euler problem using an order-4 symplectic integrator, which conserves the Hamiltonian. We used this integrator to simulate the restricted Euler problem and recovered known orbits from the literature.