The problem of optimal control of the orientation of an orbit of a spacecraft as a deformable figure

The problem of optimal control of the orbit orientation of a spacecraft regarded as a deformable figure is studied. The problem of optimal re-orientation of an orbit is formulated as a problem of optimal control of the motion of the center of mass of a spacecraft with a movable right end of the trajectory and is solved based on the Pontryagin maximum principle. To describe the orientation of an instantaneous orbit, a new quaternion osculating element that replaces three classical angular elements of the orbit is applied. Necessary optimality conditions are obtained; several first integrals of the system of equations of the boundary-value problem of the maximum principle are found; transformations that reduce the dimension of the system of differential equations of the boundary-value problem (without their complication) are proposed; the proposed approach is analyzed, and an example of numerical solution of the problem is presented.