Reversible Adaptive Regularization: Perturbed Kepler Motion and Classical Atomic Trajectories

Reversible and adaptive integration methods based on Kustaanheimo-Stiefel regular-ization and modiied Sundman transformations are applied to simulate general perturbed Kepler motion and to compute classical trajectories of atomic systems (e.g. Rydberg atoms). The new family of reversible adaptive regularization (RAR) methods also conserve angular momentum and exhibit superior energy conservation and numerical stability in long time integrations. The schemes are appropriate for scattering, for astronomical calculations of escape time and long-term stability, and for classical and semiclassical studies of atomic dynamics. The components of an algorithm for trajectory calculations are described. Numerical experiments illustrate the eeectiveness of the reversible approach.