Motion with a constant velocity modulus in a central gravitational field

✍ Scribed by Yu.F. Golubev

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 782 KB
• Volume: 66
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(02)00141-7

✦ Synopsis

The problem of the motion of a particle (point mass) with a constant velocity modulus in a Newtonian central gravitational field is investigated by two methods: using Lagrange's equations with a multiplier, and using the equations of dynamics proposed earlier [1] for systems with non-holonomic constraints that are non-linear with respect to velocities, A phase diagram of the motion is constructed. The structure of the trajectories as a function of the initial conditions is investigated. Formulae in the form of quadratures are obtained for calculating the time of motion along the trajectory and the angular distance of flight. A qualitative analysis of the properties of improper integrals expressing the angular distance is presented. These properties are illustrated by the results of a numerical investigation. The possibility of carrying out elementary manoeuvres in the vicinity of an attracting centre are analysed.