Near-integrability as a numerical tool in solar system dynamics

Observatory, PO Box 14, 00014 University of Helsinki, Finland

Corresponding author: M. Kaasalainen, Mikko.Kaasalainen@astro.helsinki.fi

Received: 4 February 2000
Accepted: 11 December 2000

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.