Reduction of Low-Thrust Continuous Controls for Trajectory Dynamics

A novel method to evaluate the trajectory dynamics of low-thrust spacecraft is developed. The thrust vector components are represented as Fourier series in eccentric anomaly, and Gauss's variational equations are averaged over one orbit to define a set of secular equations. These secular equations are a function of only 14 of the thrust Fourier coefficients, regardless of the order of the original Fourier series, and are sufficient to accurately determine a low-thrust spiral trajectory with significantly reduced computational requirements as compared with integration of the full Newtonian problem. This method has applications to low-thrust spacecraft targeting and optimal control problems.