Finding analytic solutions on active arcs of the optimal trajectory in a gravitational field and their applications

We consider a method for finding partial solutions for the optimal motion problem of a space vehicle in a central Newtonian field on intermediate thrust arcs. This is the Lehmann-Filhés method based on knowing an incomplete integral of the Hamilton–Jacobi equations. With this method, we obtain a number of partial solutions that can be applied to solving practical problems of space flight mechanics. As an example, we solve the problem of rotating the axis of an elliptical orbit. We compare characteristic velocities necessary to rotate the axis of an elliptical orbit.