Geometric mechanics and the dynamics of asteroid pairs

Abstract

The geometric mechanics of a pair of asteroids in orbit about each other under mutual gravitational attraction was analyzed using Lagrangian reduction. The technique rely on a specific choice of connection, whose curvatures leads to Coriolis effects, as well as critical for carrying out sharp stability analysis and a geometric phase analysis. The configuration space of a single asteroid was the Euclidean group. It was observed that the technique is essential in carrying out the dynamical system analysis of tube and lobe dynamics.