Abstract

This thesis analyzes the dynamics of the Planar (2+2)-Body Problem which consists of two asteroids moving under the gravitational force of each other and of two larger primaries. We use the McGehee blow up technique to remove the singularities in the dynamics associated with a triple collision with one of the primaries by introducing a new set of variables. Additional variables are introduced to reduce the dimension of the problem. We then derive the dynamics for these new variables. We then use the energy relation that comes from the original Hamiltonian to describe the collision manifold which is pasted in at the singularity associated with triple collision. We derive the dynamics on the collision manifold and prove several properties including the presence of gradient-like flow, the presence of 6 equilibrium points, and the stability at each of these points.

Degree

College and Department

Mathematics; Computational, Mathematical, and Physical Sciences

Rights

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