Motion of a particle with a constant module of velocity in the newtonian field of gravity

The problem on a motion of a particle with a constant module of velocity in the Newtonian field of gravity is investigated. The solution is reduced to quadratures by two ways: by means of Lagrange equations with a multiplier and by means of dynamics equations proposed in [1] for systems with nonholonomous constraints which are nonlinear relatively of velocities. The phase diagram of the motion is drawn. The dependence of trajectories structure on initial conditions is investigated. A possibility of accomplishment of simplest maneuvers in a neighborhood of the center of gravity is analyzed.