Time-Regularized Explicit Symplectic Integrators for Multibody Astrodynamics

Hamiltonian mechanics provides the foundations for analytical approaches and geometric insights into solutions for a variety of mechanical systems that are difficult to capture through alternative approaches. These insights are particularly valuable for the development of perturbation methods in astrodynamics. While explicit symplectic integrators are well established for systems with separable Hamiltonians, their application to nonseparable Hamiltonian systems, such as the circular and elliptic restricted three-body problems, has traditionally been considered intractable until a recent breakthrough by the authors. This paper generalizes this explicit symplectic integrator framework by introducing a variable time-step implementation using time regularization transformations. Numerical experiments demonstrate excellent preservation of the geometric properties of the Hamiltonian flow through the time-regularized symplectic framework, while achieving robust long-term numerical performance. The proposed scheme compares favorably with conventional nonsymplectic adaptive stepping methods, achieving higher accuracy with fewer integration steps over long-duration propagations. In particular, the symplectic framework maintains bounded energy errors, ensuring that propagated trajectories remain on the correct energy surface, which is essential for reliable orbit prediction and mission design in cislunar space.