Formation Flight with Generating Functions: Solving the Relative Boundary Value Problem

The relative motion of a formation of spacecraft is studied. Using the Hamiltonian description q;p; H(q;p; t) and solving for the generating functions for canonical transformations allows us to describe motion in the vicinity of a nominal trajectory as the solution to a two-point boundary value problem. We put some properties of such motion into relief before identifying an algorithm to solve this problem. The technique we are developing is suitable for use in designing and optimizing the nonlinear relative motion of a formation of spacecraft within a very general orbital setting.