Transfer orbit design and control based on forbes' assumption

In order to meet the requirements of space operation, the spacecrafts must maneuver agilely with the artifical propulsion. The orbit under artificial control is termed as Non-Keplerian orbit which does not follow Kepler's Laws. The transfer orbit design under the continuous thrust is one of the most important topics in this new field. Shape-based method for Non-Keplerian orbit design is developed in this paper. Firstly, the equations of motion are established in polar coordinates system. And then the nondimensional variables are introduced for computation accuracy and speed, which give rise to nondimensional equations of motion. The general equation is derived with which common curves could be utilized in orbit design. In addition, the orbit design method is described based on Forbes' velocity assumption and the formulation of the radius r with respect to time t, which is a sinusoidal function. The determination of the coefficients causes the orbit design problem to translate into an orbit control problem. The requisite thrust magnitude and direction are available via the simplified nondimensional equations of motion. In the end, an example of the transfer orbit is given. The result demonstrates that the shape-based method is feasible for the transfer orbit design or control problem under the continuous thrust, and the fuel expenditure is practicable.