On critical values concerning the evolution of the long period families

Details On critical values concerning the evolution of the long period families On critical values concerning the evolution of the long period families

Apr 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009raa.....9..494h&link_type=abstract

Research in Astronomy and Astrophysics, Volume 9, Issue 4, pp. 494-500 (2009).

Astronomy and Astrophysics

Astrophysics

Scientific paper

In a previous paper, we proposed another special critical value concerning the evolution of the long period family around the equilateral equilibrium points, besides the two values given by Henrard. Are there any other special critical values? After studying the stability curves of the long period family carefully, we gave a negative answer. During the study, we found an interesting family of periodic orbits which we called the homo family. We studied the evolution of this family following the increase of μ. With these findings, we were able to explain the origin of the four branches of periodic families emanating from L4 and the stability results of the equilateral equilibrium points.

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