Investigation of the problem of optimal correction of angular elements of the spacecraft orbit using quaternion differential equation of orbit orientation

In this paper we consider the problem of optimal correction of angular elements of the spacecraft orbit. Control (jet thrust vector orthogonal to the plane of the orbit) is limited by absolute value. The combined quality functional characterizes the amount of time and energy consumption. With the help of the Pontryagin maximum principle and quaternion differential equation of the spacecraft orbit orientation, we have formulated differential boundary value problem of correction of the angular elements of the spacecraft orbit. Optimal control law, transversality conditions, not containing Lagrange multipliers, examples of the numerical solution of the problem are given.