Near-integrability as a numerical tool in solar system dynamics
Earth and Planetary Astrophysics
2014-03-05 v1
Abstract
We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of orbital elements, we use the phase-space coordinates the object would have at a given point in its (Keplerian) orbit if the perturbing forces were removed. This formulation is suitable for almost any numerical integrator; thus, multistep schemes are easy to build, stepsize can be adjusted, and dissipative forces are allowed. Compared with traditional non-symplectic N-body integrators, the approach often offers increase in speed or accuracy if perturbations are small.
Cite
@article{arxiv.1403.0717,
title = {Near-integrability as a numerical tool in solar system dynamics},
author = {Mikko Kaasalainen and Teemu Laakso},
journal= {arXiv preprint arXiv:1403.0717},
year = {2014}
}