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Cruising in a central force field. (English) Zbl 1062.37061
Summary: We study a particle in a central force field which has a 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.

MSC:
37J60 Nonholonomic dynamical systems
70F25 Nonholonomic systems related to the dynamics of a system of particles
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
70F05 Two-body problems
70F15 Celestial mechanics
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