 
Summary: Kyoto Dynamics Days 4
Mechanics and Dynamics
December 1718, 2004
Department of Mathematics, Kyoto University
 Program 
December 17
2:003:00 Richard Montgomery (Univ. California, Santa Cruz)
New periodic orbits for the Nbody problem
ABSTRACT: In December 1999 Alain Chenciner and the speaker ``rediscovered'' a new periodic
orbit for three equal masses moving in the plane according to Newton's laws of gravity. Chris Moore
found the orbit numerically in the early 1990s, using some of the same ideas. The three equal masses
chase each other around a fixed analytic figure eight shaped planar curve. We describe the method
of proof and how it led to a whole host of new orbits for the Nbody problem. The tools of the proof
are a combination of calculus of variations, differential geometry and symmetries. The chief technical
difficulty is avoiding collisions. After a sketch of the existence proof, we will survey some
subsequently discovered orbits.
3:154:15 Toshiaki Fujiwara (Kitasato Univ.)
Synchronized Similar triangles for Planar ThreeBody Orbit
ABSTRACT: If a threebody orbit has zero angular momentum and constant moment of
inertia, the triangle whose vertexes are the positions of masses and the triangle whose
