Resonance and chaos. I. Firstorder interior resonances.
Abstract
Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted threebody problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincar e surfaces of section with a mass ratio of 10^3^ (similar to the JupiterSun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the `evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. On theoretical grounds the maximum libration width of firstorder resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 March 1997
 Bibcode:
 1997A&A...319..290W
 Keywords:

 CHAOS;
 CELESTIAL MECHANICS;
 MINOR PLANETS