PORTUGALIAEMATHEMATICA
Vol. 61, No. 3, pp. 259-280 (2004)
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PORTUGALIAE MATHEMATICA Vol. 61, No. 3, pp. 259-280 (2004) |
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Cruising in a central force fieldStanislav Furta and Gaetano ZampieriDept. of Management, Higher Commercial Management School,Levoberezhnaya St. 32, 125475 Moscow -- RUSSIA E-mail: stanislav.furta@mail.com Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, I-10123 Torino -- ITALY E-mail: gaetano.zampieri@unito.it Abstract: We study a particle in a central force field which has a \textsl{cruise motion}, namely which is constrained to keep a constant kinetic energy. It is an integrable dynamics. We describe the global geometry of the problem by introducing special variables and a new time. This permits us to prove some general facts such as the existence and the orbital stability of circular motions. As an application a Bertrand-like problem is solved. Moreover, some noteworthy potential functions are dealt with as the Newton gravity of a single celestial body. Keywords: nonholonomic dynamics; central force fields. Classification (MSC2000): 37J60, 70F25, 70H06. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2004 Sociedade Portuguesa de Matemática
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