We exhibit multiple periodic, collision-based orbits of the Newtonian n-body problem. Many of these orbits feature regularizable collisions between the masses. We demonstrate existence of the periodic orbits after performing the appropriate regularization. Stability, including linear stability, for the orbits is then computed using a technique due to Roberts. We point out other interesting features of the orbits as appropriate. When applicable, the results are extended to a broader family of orbits with similar behavior.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Simmons, Skyler C., "Analysis of Multiple Collision-Based Periodic Orbits in Dimension Higher than One" (2015). Theses and Dissertations. 5584.
Newtonian n-body problem, collision, regularization, stability, linear stability, Sitnikov problem