Solving Relative Two-Point Boundary Value Problems: Spacecraft Formulation Flight Transfers Application

Abstract

The dynamics of reconfiguration of a formation of spacecraft is studied. The problem is posed 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. An algorithm is presented that solves this problem for reconfiguration about a nominal trajectory in arbitrary gravity fields, providing a nonlinear analytical solution to this problem in the spatial domain. The technique being developed is based on a novel application of Hamiltonian dynamics, generating functions, canonical transformations, and the Hamilton‐Jacobi equation. A specific example of reconfiguration of spacecraft about an Earth‐sun libration point is studied that shows that the optimal transfer time depends strongly