Motion of a Particle with a Constant Module of Velocity in the Newtonian Field of Gravity.

Abstract:

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 \citegolubev 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.