Explicit Symplectic Integrators for Cislunar Regimes

Hamiltonian mechanics provides the mathematical foundations for analytical solutions and geometric insights into a range of mechanical systems that remain elusive through alternative methods. These rich insights conjoined with perturbation theory provide valuable avenues for computing approximate solutions for astrodynamics problems. In numerous instances documented in the literature, separable Hamiltonians can use explicit symplectic integrators, such as the Störmer Verlet method, to preserve phase space and the underlying constants of motion during numerical propagation. This paper establishes a crucial result that there exists a broad class of nonintegrable dynamic systems that include both the circular and elliptic restricted three-body problems wherein the Hamiltonian is nonseparable; it is indeed possible to realize explicit symplectic integrators. Furthermore, our numerical analysis in this paper confirms that using these explicit symplectic integrators provides computational accelerations and improved numerical stability for long-term state propagation and maintaining first integrals when compared with conventional nonsymplectic approaches.