Numerical computation of optimal atmospheric trajectories involving staged vehicles

A trajectory optimization procedure is described which can solve practical problems involving staged vehicles or discontinuous equations of motion. It is an extension of a computer code called CTOP (Chebychev Trajectory Optimization Program) which was described by Hargraves et al. (1981). With CTOP, the state and control variables are described as functions of time by patched polynomials. A subset of the patch points (including initial and final time) may be designated as free parameters called events. It is pointed out that discontinuities may occur at events and that the payoff may depend on them. The values of the events are adjusted in order to achieve the desired optimum. Numerical examples are presented.