EDP Sciences
Free access
Volume 368, Number 2, March III 2001
Page(s) 706 - 711
Section Celestial mechanics and astrometry
DOI http://dx.doi.org/10.1051/0004-6361:20010002

A&A 368, 706-711 (2001)
DOI: 10.1051/0004-6361:20010002

Near-integrability as a numerical tool in solar system dynamics

M. Kaasalainen and T. Laakso

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

(Received 4 February 2000 / Accepted 11 December 2000 )

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.

Key words: methods: numerical -- celestial mechanics -- solar system: general

Offprint request: M. Kaasalainen, Mikko.Kaasalainen@astro.helsinki.fi

© ESO 2001