publication . Other literature type . Preprint . Article . 2000

A remarkable periodic solution of the three-body problem in the case of equal masses

Alain Chenciner; Richard Montgomery;
Open Access
  • Published: 01 Nov 2000
  • Publisher: JSTOR
Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is that the three bodies chase each other around a fixed eight-shaped curve. Setting aside collinear motions, the only other known motion along a fixed curve in the inertial plane is the ``Lagrange relative equilibrium" in which the three bodies form a rigid equilateral triangle which rotates at constant angular velocity within its circumscribing circle. Our orbit visits in turns every ``Euler configuration" in which one of the bo...
free text keywords: Mathematics - Dynamical Systems, Statistics, Probability and Uncertainty, Statistics and Probability

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