An improved indirect method for in plane orbit optimization under constant thrust

The transfer of a spacecraft between coplanar orbits under continuous constant thrust with minimum fuel consumption was investigated. A control equation of the optimal trajectory, which the steering angle must satisfy, was derived by using maximum principle. Combining the control equation with dynamic equations, we establish an improved indirect method to design optimal coplanar transfer orbit and propose an approximate application method for the condition when thrust direction adjustment ability was limited. Due to avoiding solving the Lagrange costate differential equations, the improved indirect method reduces difficulty of initial value estimation and calculation a lot than traditional indirect method. Compared with Gauss pseudospectral method, the improved indirect method can get higher precision and better numerical smoothness. Simulations show that a limitation on the magnitude of the second derivative of thrust angle can improve change law of thrust angle and reduce change range of thrust angle; as to the fuel consumption, the greater the thrust magnitude is, the more the fuel consumption is, and the optimal transfer orbit can save fuel consumption a lot under a certain large magnitude of thrust.