OPTIMAL COPLANAR ORBIT TRANSFER IN LEVI CIVITA COORDINATES

This paper addresses optimal planar orbit transfers using Levi-Civita coordinates through continuation. The Levi-Civita coordinates is a useful orbit representation due to the fact that, for a body traveling through a trajectory with fixed semi-major axis, the equations of motion for these coordinates are represented by linear dynamics. In fact, the solution to the unperturbed EOM it that of a simple harmonic oscillator with the oscillation frequency as function of the semi-major axis itself. Another relevant aspect of Levi-Civita coordinates is that the unperturbed dynamics presents equally segmented position steps for fixed time step segments, which makes fixed step numerical propagation easier for highly eccentric orbits. These properties of the Levi-Civita coordinates motivate this work, which uses Sequential Quadratic Programming to obtain optimal coplanar orbit transfer in these coordinates. We apply the optimization method to different orbit transfer scenarios and evaluate the performance of the algorithm. The near-linear characteristics of Levi-Civita allows Sequential Quadratic Programming methods to converge quickly and reliably if there is tolerance for slight errors in the final orbital elements.