Indirect optimal technique for low-thrust trajectory design in deep-space exploration

The optimal technique for low-thrust trajectory optimization is concerned in this paper. In solar ecliptic coordinate, a normalized three-dimensional orbit transfer model was introduced; the optimal direction of thrust was obtained with linear combination of co-state variables while the Hamiltonian and co-state equations were also established. A switching function was introduced according to Pontryagin's Maximum Principle. The example of fuel-optimal flyby problem from the Earth to an asteroid via Mars gravity assist was given showing that gravity assist can supply extra velocity to save much of fuel.