Physical Sciences and Mathematics Commons^™

Novel N-Body Orbits For Constrained Potentials Including The Unusual Figure Eight Three Body Orbit, Jan M. Dudzik

Masters Theses

Recently new n-body planar orbits have been discovered which are known as choreographies. These orbits correspond to small n, generally n<20, and exhibit unexpected patterns with respect to given initial conditions. Here we shall examine numerical solutions to the three-body problem and the restricted three-body problem for three body potentials that are the sum of three two-body potentials. Then for an everywhere attractive three body potential with non-collinear and collision-less orbits with a strictly monotone decreasing potential function there exist bound states that are not chaotic that are choreographies. For the right initial conditions these orbits can be mapped numerically and visualized. We will display a number of these cases corresponding to the three body problem, restricted three body problem, the chaotic restricted three body problem and the new figure eight bound state choreography for the Kazalov potential orbits to exhibit some of their special features and to take note of a number of open questions dealing with simple orbital problems.