Canonical transformation applications to optimal trajectory analysis.

In the following treatment, some applications of canonical transformation theory to the analysis of optimal trajectories for space vehicles are described. As a consequence of performing a sequence of canonical transformations, a closed-form solution to the coast-arc problem can be obtained by evaluating a single indefinite integral. A complete solution is derived for the case of elliptical motion, and this solution does not require a modification for circular conditions. Further, since the integration constants are canonic constants, they can be used to define a base solution for canonical perturbation approaches to the problem of describing the optimal motion of a low-thrust space vehicle. The canonic constants are especially useful for near-circular missions since they are functions of the classical Poincare variables. The complete solutions of the Hamilton-Jacobi equation for the parabolic and hyperbolic coast-arc solutions are given and a convenient method for transforming the Lagrange multipliers is also presented.