Chen, Nai-Chia2014-10-202014-10-202014-08https://hdl.handle.net/11299/166977University of Minnesota Ph.D. dissertation. August 2014. Major: Mathematics. Advisor: Richard Moeckel,. 1 computer file (PDF); vi, 86 pages.The thesis is devoted to finding periodic brake orbits in the N-body problem. We consider certain subsystems of the N-body problem that have two degrees of freedom, including the isosceles three-body problem and other highly symmetric sub-problems. We prove the existence of several families of symmetric periodic orbits, including ``Schubart-like" orbits and brake orbits, by using topological shooting arguments.enCelestial mechanicsClassical mechanicsDifferential equationsN-body problemMathematicsThesis or Dissertation