Publication Date

2023

Document Type

Conference Poster

First Advisor

McCord, Chris

Department

Department of Computer Science| Department of Mathematical Sciences

Abstract

The N-body problem, first proposed by Isaac Newton, is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It has significance to many areas of science, including physics and computer science, and is crucial in understanding how the universe works. In fact, it was a primary motivation for Newton's development of calculus. An important application of the N-body problem is within celestial mechanics and involves how planets and other celestial bodies move with mutual gravitational attraction. It is important in developing how satellites behave in space using complicated orbits, which are sent out to give us television, predict the weather, and understand our solar system. As particles move, their position and velocity change, but energy and angular momentum are conserved. Level sets of constant energy and angular momentum, known as integral manifolds, represent constraints of movement to a system. For different levels of energy, the geometry of the integral manifold can change. There are energy levels where the geometry has an abrupt, quantitative change, known as bifurcation energy levels. Bifurcation values depend on the different ways the particles can form “central configurations''; configurations or arrangements of equal masses on a three-dimensional plane which retain their shape if released simultaneously from rest. We study the patterns of "finite" vs. "infinite" bifurcations using available data on central configurations and an algorithm developed by Alain Albouy, who identified those two categories of singular values of energy. We show that the conjecture that all bifurcations at infinity occur at energy levels less in magnitude than the finite bifurcations, is false.

Comments

This poster placed 3rd in Math and Computational Sciences at 2023 CURE.

Program

Conference on Undergraduate Research and Engagement: Math and Computational Sciences

Publisher

Northern Illinois University

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