Three Classes of Newtonian ThreeBody Planar Periodic Orbits
Abstract
We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic threebody orbits into families, which fall into four classes, with all three previously known families belonging to one class. The classes are defined by the orbits’ geometric and algebraic symmetries. In each class we present a few orbits’ initial conditions, 15 in all; 13 of these correspond to distinct orbits.
 Publication:

Physical Review Letters
 Pub Date:
 March 2013
 DOI:
 10.1103/PhysRevLett.110.114301
 arXiv:
 arXiv:1303.0181
 Bibcode:
 2013PhRvL.110k4301S
 Keywords:

 45.50.Jf;
 05.45.a;
 95.10.Ce;
 Few and manybody systems;
 Nonlinear dynamics and chaos;
 Celestial mechanics;
 Physics  Classical Physics
 EPrint:
 to be published in Phys. Rev. Lett.