<h2>AAS 99-128</h2>
<h2>Optimal Spacecraft Trajectories Via Higher Order Differential Inclusions                                                                         </h2>
<h4>V. Coverstone-Carrol*, C.A. Hartman*, A.L. Herman**, D.B. Spencer***                                                                                                                </h4>
*U. Illinois, Urbana-Champaign,**Spectrum-Astro, Gilbert, AZ, ***USAF Research Lab, Kirtland AFB, NM                                                                      
<h2> Abstract </h2>
Higher order differential inclusion (HODI) is a new modeling technique that is applied to the modeling and optimization of spacecraft trajectories. The spacecraft equations of motion are mathematically manipulated into differential constraints that remove explicit  appearance of the control variables (e.g., thrust direction and magnitude) from the problems statement. These constraints are transformed into a nonlinear programming problem by using higher order approximations of the derivatives of the states. In this work, the new method is first applied to a simple example to illustrate the technique and then to a three-dimensional, propellant-minimizing, Low-Earth-Orbit to Geosynchonous-Earth-Orbit spacecraft transfer problem. Comparisons are made with results obtained using an established modeling technique.