Abstract

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.

Degree

PhD

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2015-06-01

Document Type

Dissertation

Handle

http://hdl.lib.byu.edu/1877/etd8710

Keywords

Newtonian n-body problem, collision, regularization, stability, linear stability, Sitnikov problem

Included in

Mathematics Commons

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