FORMATION FLIGHT WITH GENERATING FUNCTIONS: the dynamics of spacecraft reconfiguration

The dynamics of reconfiguring a formation of spacecraft is studied. We pose the problem as a two-point boundary value problem where the initial and final positions and times are known and the necessary velocities for the reconfiguration transfers must be found. We present an algorithm that solves this problem for reconfiguration about a nominal trajectory in arbitrary gravity fields, providing a non-linear analytical solution to this problem in the spatial domain. The technique we are developing is based on a novel application of Hamiltonian dynamics, generating functions, canonical transformations and the Hamilton-Jacobi equation. A specific example of reconfiguring spacecraft about an Earth-Sun libration point is studied, showing that the optimal transfer time depends strongly on the initial and final positions. Graduate Research Assistant, PhD Candidate, Aerospace Engineering Department, FXB Building, 1320 Beal Avenue, Ann Arbor, MI 48109-2140, [email protected] Associate Professor, Senior member AIAA, Aerospace Engineering Department, FXB Building, 1320 Beal Avenue, Ann Arbor, MI 48109-2140, [email protected]