Optimal space trajectories with multiple coast arcs using modified equinoctial elements
This paper is devoted to spacecraft trajectory optimization problems. It starts with description of orbit dynamics, equations of motion and spacecraft eclipse condition. Then, for minimum-time trajectories with eclipse intervals formulated as a multiple-arc optimization problem, necessary optimality conditions are derived. These conditions contain Pontryagin Minimum Principle, the adjoint equations for costate variables, the related boundary conditions, the transversality relations of the final value of the Hamiltonian and the multipoint necessary optimality conditions at the junction times between two arcs. The author shows that all the multipoint conditions can be solved in the sequential way. Numerical example is presented showing the effectiveness of the approach proposed in the paper. Further, minimum-fuel trajectories problem is considered and necessary optimality conditions for that problem are derived. Modified equinoctial elements such as elliptic, parabolic and hyperbolic arcs are used to describe the spacecraft dynamics. Also the closed form of the costate along optimal coast arcs are obtained with the use of the Mathematica software. The paper contains an ample set of relevant references consisting of 50 items.
scientific article; zbMATH DE number 7436668