Structure of the 3:1 Jovian resonance

Title:              Structure of the 3:1 Jovian resonance - A comparison
                    of numerical methods
Authors:            MURRAY, C. D.; FOX, K.
Affiliation:        AB(Queen Mary College, London, England)
Journal:            Icarus (ISSN 0019-1035), vol. 59, Aug. 1984, p.
                    221-233. Research supported by the Science and
                    Engineering Research Council of England.
Publication Date:   08/1984
Origin:             STI
Category:           Lunar and Planetary Exploration
NASA/STI Keywords:  ASTEROIDS, JUPITER (PLANET), RESONANCE, SUN, THREE
                    BODY PROBLEM, ECCENTRICITY, EQUATIONS OF MOTION,
                    MAPPING, ORBITS, TRAJECTORIES
Bibliographic Code: 1984Icar...59..221M

Abstract

The motion of asteroids near the 3:1 Jovian resonance in the restricted planar case is studied using three numerical methods: (1) integrating the full equations of motion, (2) integrating the averaged equations of motion, and (3) using an algebraic mapping recently developed by Wisdom (1982). The three methods are examined in detail, including their relative merits. The regular and chaotic regions in two starting planes near the 3:1 resonance are determined, and the three methods are then applied to the study of regular and a chaotic trajectory. The divergence of the solutions as the eccentricity increases is demonstrated, and the effect on the averaging method of the inclusion of fourth-order terms in the Hamiltonian is examined.

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