Masters Thesis Presentation - Jasper Andringa

Title: Central Configurations in the N-Body Problem with Generalized Potential

Abstract:

Central configurations are configurations of n point masses, in which each body’s acceleration points towards the centre of mass and is proportional to the distance from it. From one central configuration one can construct a family of homographic solutions: solutions which change only through uniform rotation and scaling. This thesis generalizes the potential under which central configurations are usually studied, by moving from the Newtonian potential to the harmonic potential and general homogeneous potentials. We largely follow Moeckel’s notes for the Newtonian case. We establish central configurations, derive conditions for homographic solutions and prove existence of central configurations for any choice of n masses. For the harmonic potential, we find that every configuration is a central configuration, which is a consequence of the linearity. The homographic solutions turn out to satisfy the harmonic oscillator equations. For the general homogeneous potential we also find the conditions for homographic solutions, show existence, and count the number of collinear configurations by stating a generalized version of Moulton’s theorem. We finish with some simulations of homographic solutions of 3-body systems.

Supervisors: Holger Waalkens, Alef Sterk