On evolutionary motions of a particle in a gravitational field
Non-conservative, time-periodic perturbations of the Kepler problem are studied. A phase-averaged system is given, which determines the evolution in the system when there are no resonance modes. The qualitative behaviour of the solutions in the resonance zones is studied. Depending on the structure of the behaviour of the solutions, the resonances are divided into traversable, partially traversable and non-traversable. The boundedness of the set of partially traversable resonances is established, and this, in many cases, makes it possible to determine evolution in a system with resonance modes. An example is used to illustrate the method. It is shown that a constant component in the periodic function of the perturbation causes the evolutionary process to become non-unidirectional.
Non-conservative, time-periodic perturbations
scientific article; zbMATH DE number 4022681