Long-Period Effects in Nearly Commensurable Cases of the Restricted Three-Body Problem

Details Long-Period Effects in Nearly Commensurable Cases of the Restricted Three-Body Problem Long-Period Effects in Nearly Commensurable Cases of the Restricted Three-Body Problem

Apr 1964

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1964saosr.149.....s&link_type=abstract

SAO Special Report #149 (1964)

Computer Science

67

Scientific paper

The author has applied the ideas of Poincaré to a study of the long-period effects in nearly commensurable cases of the restricted three-body problem. After isolating the secular and critical terms of the disturbing function by a numerical averaging process performed on an IBM 7094 computer, he found stability for all real asteroid orbits corresponding to the cases treated here. Periods of the variations are given for some forms of planar motion. The theory indicates planar and nonplanar periodic solutions. No evidence is found for a disintegration of the Trojan and Hilda groups of asteroids. This work supports Brouwer's explanation of differences between the Hecuba and Hilda commensurabilities.

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