Mathematics Colloquia and Seminars

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Figure eights with three bodies


Speaker: Prof. Richard Montgomery, UC Santa Cruz
Location: 693 Kerr
Start time: Mon, May 22 2000, 4:10PM

Recently, Alain Chenciner (Paris 7 and Bureau des Longitudes, France) and the speaker discovered a surprisingly simple periodic orbit for the Newtonian three body problem : three equal masses chase each other around a fixed curve in the plane with the shape of a figure eight. From many points of view this eight is the simplest periodic solution for the problem, after those of Lagrange and Euler. We outline our existence proof, which combines the direct method of the calculus of variations, the use of discrete symmetries and a detailed knowledge of the geometry of space of oriented congruence classes of planar triangles. We also describe some of Carles Simos (of University of Barcelona, Spain) recent numerical investigations. He has found that our orbit is KAM-stable and that it is the first member of a collection of infinite families of orbits in which N masses moving under their mutual gravitational attraction travel along a fixed planar curve in the shape of eights, or chains, or flowers, as well as more complicated curves.

note: Cookie and Coffee at 3:45pm