Approximate on-off low-thrust space trajectories using fourier series

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A new development on the method of constructing approximate space trajectories using finite Fourier series shape-based (FFS-SB) was proposed. This FFS-SB method provides an initial trajectory that satisfies given thrust constraints and EoM at discrete points, as well as the boundary conditions (BCs). Besides the fast construction of space trajectories that satisfy given thrust constraints, the proposed method has the capability of generating on/off thrust profiles. For every different selection of the Fourier coefficients, a different shape is obtained. This was possible by forcing the constraint slack variables to take only one of three discrete values. The drawback is that the computational time of the proposed on/off thrust finite Fourier series trajectory approximation is 3-4 orders of magnitude higher than that of the original finite Fourier series trajectory approximation method.

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Journal of Spacecraft and Rockets