Motion with a constant velocity modulus in a central gravitational field |
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Authors: | Yu F Golubev |
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Institution: | , Moscow, USSR |
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Abstract: | 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. |
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