<h2>AAS 95-422</h2><h2>The Use of Nonsingular Elements In Trajectory Optimization In Terms of True Longitude</h2><h4>J. A. Kechichian, Aerospace Corporation, Los Angeles, CA</h4><h2> Abstract </h2>The system and adjoint differential equations needed to solve low-thrust transfer and rendezvous trajectories are derived in terms of nonsingular orbit elements with the true longitude selected as the sixth variable as well as the variable that defines the radial distance.  The perturbation accelerations are resolved in the rotating polar frame such that the equations of motion are written in polar coordinates.  This formulation is particularly convenient for the consistent treatment of the J2 perturbation whose components are easily expressed in terms of the true longitude.  The iterations needed for the solution of Kepler's equation are also eliminated and the analytic form of the adjoin equations provided in their simplest aspect thus far.<br><br>