Central potentials with closed cruise orbits |
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Authors: | Gianluca Gorni |
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Institution: | a Università di Udine, Dipartimento di Matematica e Informatica, via delle Scienze 208, 33100 Udine, Italy b Università di Verona, Dipartimento di Informatica, strada Le Grazie 15, 37134 Verona, Italy |
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Abstract: | A particle will be said to be in cruise motion if it is nonholonomically constrained to have constant speed. When the particle is placed in a central force field, the resulting mechanical system is known to be integrable. Cruise orbits in a central force field may be closed (periodic in time) or not, depending on the potential and on the speed. Here we give a constructive characterization of all central potentials for which all cruise motions of a given speed are closed. As a consequence, we also give a new proof of the fact that for any such potential the set of speeds for which all cruise motions are closed has always empty interior. |
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