2010 Student Research Conference:
23rd Annual Student Research Conference

A Computational Study of Lagrangian Points and Stability in The Restricted Three Body Problem
Garrett C. McCormack
Dr. Todd Palumbo, Faculty Mentor

The restricted three-body problem is historically significant and remains open to this day. This project investigates the orbital stability of a third body in the planar restricted three body problem by exploring the behavior of an infinitesimal mass near the Lagrangian points of a two body system of varying mass ratios and eccentricities of orbit. Using numerical methods we record the behavior of the infinitesimal mass in a grid of initial positions in order to create maps of the regions of stability and instability in the proximity of the Lagrangian points and the center of mass of the system. We perform our computations using a rotating-pulsating coordinate system and a high precision numerical algorithm for accurate simulations of the orbit of the infinitesimal mass. Ongoing research includes investigation of increasing computational performance of numerical methods for the restricted three body problem using parallel processing on the CUDA architecture.

Keywords: Lagrangian Points, Stability, Chaos, Numerical Methods, Numerical Algorithm, Orbits, Three-Body Problem, Three-Body System

Topic(s):Mathematics
Physics
Computer Science

Presentation Type: Poster

Session: 2-4
Location: SUB-GEO
Time: 4:15

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