RELATIVE SATELLITE MOTION SOLUTIONS USING CURVILINEAR COORDINATE FRAMES

A novel set of solutions for satellite relative motion is developed. Using nonlinear transformations from a cylindrical and spherical coordinate frame to a Cartesian coordinate frame, nonlinear satellite relative motion equations can be derived. These nonlinear representations better capture the curvature and relative dynamics of an orbit due to the nature of curvilinear coordinate frames. Approximate solutions are also derived using a 2nd order Taylor series expansion of the nonlinear equations. These 2nd order approximate solutions are compared analytically to the Quadratic Volterra solution. Example trajectories are generated and compared using the novel set of solutions and the Quadratic Volterra solution. These novel solutions can be used for many different satellite relative motion applications such as initial relative orbit determination algorithms and maneuver/targeting applications.