Symplectic Maps for the nBody Problem: Stability Analysis
Abstract
The stability of new symplectic nbody maps is examined from the point of view of nonlinear dynamics. The resonances responsible for the principal artifacts are identified. These are resonances between the stepsize and the difference of mean motions between pairs of planets. For larger stepsizes resonant perturbations are evident in the variation of the energy of the system corresponding to these stepsize resonances. It is shown that the principal instability of the method can be predicted and corresponds to the overlap of the stepsize resonances. It is noted that the analysis suggests that other artifacts will occur. For example, the overlap of a stepsize resonance with a resonance of the actual system may also give a region of chaotic behavior that is an artifact. It is pointed out that the fact that the principal artifacts corresponds to a particular set of stepsize resonances suggests that it may be possible to perturbatively remove the effect when the stepsize resonances are nonoverlapping.
 Publication:

The Astronomical Journal
 Pub Date:
 November 1992
 DOI:
 10.1086/116378
 Bibcode:
 1992AJ....104.2022W
 Keywords:

 Many Body Problem;
 Solar System Evolution;
 Computational Astrophysics;
 Systems Stability;
 Astrophysics;
 CELESTIAL MECHANICS;
 METHODS: NUMERICAL