Patched shaping approach to low-thrust multi-revolution transfer design

摘要

This paper proposes a patched shaping approach method for the problem of low-thrust multi-revolution transfers between coplanar elliptic orbits. A simple shape is proposed to solve the multi-revolution transfers between coplanar coaxial elliptic orbits with the same eccentricity. The cosine inverse polynomial shape is used to transfer between coplanar noncoaxial elliptic orbits with different eccentricities using three revolutions or less. Finally, the low-thrust multi-revolution trajectory between arbitrary coplanar elliptic orbits can be achieved by means of the patched shaping approximation, which is composed of the proposed shape and the cosine inverse polynomial shape, considering thrust magnitude constraints at patched points. The proposed shape, based on the equation of the radial component, which uses a Fourier expansion of the semimajor axis, can effectively model the low-thrust multi-revolution transfers. And the closed-form solutions of the Fourier series coefficients are determined by the boundary conditions and the trajectory safety constraints. Compared with only a single shape method, numerical results show that the proposed approach of patched shaping can be used with a shorter-transfer-time and lower cost to implement the design of low-thrust multi-revolution transfers.