Cruising in a central force field (Q1769829)

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.