So do you mean I should try to compute a case when a barbell rotate around some central point object? And compare with general solution (without a spin)?zwierz said:for a simplest example consider a barbell (two equivalent mass points linked by a weightless rod) in the gravity field of a fixed mass point. Consider a planar motion
Actually it is a very hard problem, you can find only partial results in articles, not in textbooks
The Kepler problem with spin is a mathematical model used to describe the motion of a spinning object under the influence of gravity. It is an extension of the classical Kepler problem, which only considers the motion of non-spinning objects.
The main difference between the two is that the Kepler problem with spin takes into account the rotation of the object, which adds an additional degree of freedom to the system. This means that the equations of motion are more complex and the solutions are more difficult to obtain.
The Kepler problem with spin has a wide range of applications, including the study of celestial bodies such as planets, moons, and asteroids. It is also used in spacecraft dynamics and control, as well as in the development of new satellite and orbit designs.
The Kepler problem with spin is solved using numerical methods, such as Runge-Kutta or Taylor series, due to the complexity of the equations involved. These methods allow for the calculation of the object's trajectory and other important parameters, such as its spin rate and orientation, over time.
Yes, there are many real-world examples of the Kepler problem with spin, such as the motion of planets in the solar system, the rotation of asteroids, and the attitude control of spacecraft. It is also used in sports such as figure skating and diving to model the motion of spinning athletes.