Colloquium: Skyler Simmons (Southern Utah University)

Event Details

Title: Stability of Collision-Based Periodic n-Body Problems

Abstract: The Newtonian n-body problem describes the motion of n point masses interacting with each other with gravitational force. The physical laws governing this motion were codified by Newton in his Principia in 1686. Under Newton’s laws, two colliding bodies’ velocities increase without bound as they approach collision. Levi-Civita demonstrated that through a suitable change of variables, certain collisions could be regularized, allowing the orbit to be continued past the collision. Variations on Levi-Civita’s work continue to be used in the study of collision-based orbits today. In this talk, I will present a few periodic orbits featuring collisions, describe the methods used to study their stability, and present known results about a few orbits.