Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 61, No. 3, pp. 259-280 (2004)

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Cruising in a central force field

Stanislav Furta and Gaetano Zampieri

Dept. 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.

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Electronic version published on: 7 Mar 2008.

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