A Second Order Method for Computing an Optimal Re-Entry Trajectory Using Numerical Derivatives.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
Pagination or Media Count:
The primary purpose of the study was to investigate a second order method using numerical derivatives to converge to an optimal set of initial costates that would produce an optimal re-entry trajectory. A second objective of the research was to test the computational method by computing a minimum total heat input trajectory two dimensional for a lifting body. It was assumed that the vehicle could attain a maximum lift-to-drag of 2.0 during its desent from a near earth orbit. The initial states are known, the initial costates are unknown, and only the final altitude at a fixed final range is specified. The second order method uses the first and second difference equations to iterate on corrections to an arbitrarily chosen set of initial costates. The corrections are based on minimizing a scalar terminal error function. The results indicate that the numerical integration errors limit too severely the accuracy to which the second partials of the terminal errors with respect to the initial costates could be estimated. Modified author abstract
- Spacecraft Trajectories and Reentry