Some Perturbed Keplerian Systems
We now possess all the necessary tools to study some interesting Keplerian perturbed systems: the Stark–Quadratic–Zeeman problem, the circular restricted three–body problem, and the motion of a satellite around an oblate primary. In all three cases we will first find the normal integrable form, comparing the relative motion with the “true” one obtained by numerical integration. Several concrete examples will be given, showing in general a very good agreement between the analytical and numerical results. What the normal integrable form is not able to show is the presence of resonances, which are just the indicators of nonintegrability. Then, with the Frequency Modulation Indicator (FMI) we will analyze how order, chaos, and resonances are localized in action space, thus completing the study of the three quasi-integrable systems.
KeywordsNorth Pole Kepler Problem Secondary Resonance Hyperbolic Point Unperturbed Motion
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