The problem of rendezvous of a controlled space vehicle with an uncontrolled space vehicle moving along an elliptical Keplerian orbit in the central Newtonian gravitational field

The problem of rendezvous of a controlled space vehicle with an uncontrolled space vehicle moving along an elliptical Keplerian orbit in the central Newtonian gravitational field is considered. The problem is formulated as the problem of optimal control motion of the center of mass of the controlled space vehicle with a flexible right end of the trajectory and is solved on the basis of the Pontryagin maximum principle. A new quaternion osculating orbital element, instead of three classical angular elements, is used for description of the orientation of the instantaneous orbit of the space vehicle. Necessary optimal conditions are obtained; first integrals of the system of equations of the boundary value problem of the maximum principle are found; transformations reducing the dimensionality of the system of differential equations of the boundary value problem (without their complication) are proposed; analysis of the proposed solution is given; and examples of numerical solution of the problem are presented.