Cruising in a central force field.

*(English)*Zbl 1062.37061Summary: 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 |