Families of asymmetric periodic solutions of the restricted problem of three bodies for the Sun-Jupiter mass ratio and their relationship with the symmetric families |
| |
| Authors: | D B Taylor |
| |
| Institution: | 1. H. M. Nautical Almanac Office, Royal Greenwich Observatory, Herstmonceux Castle, BN27 1RP, Hailsham, East Sussex, England
|
| |
| Abstract: | Message derived a method to detect bifurcations of a family of asymmetric periodic solutions from a family of symmetric periodic solutions in the restricted problem of three bodies for the limiting case when the second body has zero mass. This is used to examine several small integer commensurabilities. A total of 21 exterior and 21 interior small integer commensurabilities are examined and bifurcations (two in number) are found to exist only for exterior commensurabilities (q+1):1,q=1, 2,, 7. On investigating other commensurabilities of this form for values ofq up to 50 two bifurcations are still found to exist for each. The eccentricities of the two bifurcation orbits are given for eachq up to 20. For a Sun-Jupiter mass ratio the complete family of asymmetric periodic solutions associated withq=1, 2,..., 5, and the initial segments of the asymmetric family withq=6, 7,..., 12, have been numerically determined. The family associated withq=5 contains some unstable orbits but all orbits in the other four complete families are stable. The five complete families each begin and end on the same symmetric family. The network of asymmetric and symmetric families close to the commensurabilities (q+1):1,q=1, 2,..., 5 is discussed. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
