On Chenciner-Montgomery's orbit in the three-body problem

Pages: 85 - 90, Volume 7, Issue 1, January 2001

doi:10.3934/dcds.2001.7.85       Abstract        Full Text (125.1K)       Related Articles

Kuo-Chang Chen - School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States (email)

Abstract: Recently A. Chenciner and R. Montgomery found a remarkable periodic orbit for a three-body problem by variational methods. On this orbit all masses chase each other along a figure-eight circuit without any collision, and the solution curve is indeed a minimizer of the action functional on a properly chosen path space. One technical difficulty, where numerical integration had been used in their proof, is to show that the minimizing orbit does not experience any collision. In this paper a short analytical proof will be presented.

Keywords:  three-body problem, variational methods, action minimizing orbit.
Mathematics Subject Classification:  34C25, 49J27, 70F07, 70F35.

Received: June 2000;      Revised: September 2000;      Published: November 2000.