Titlebook: Geography of Order and Chaos in Mechanics; Investigations of Qu Bruno Cordani Book 20131st edition Springer Science+Business Media, New Yor

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The Kepler Problem,In this chapter, we will study the group-geometrical structure of the Kepler problem and point out how this structure also turns out to be useful in the study of the perturbed case.

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The KEPLER Program,In this chapter we will describe how to use the KEPLER program, trying to be self-contained and without referring excessively to the underlying mathematical structure. The command statements are gathered in four windows, which one selects in the pop-up menu in the left-top corner. See the Appendix A for snapshots of the MATLAB programs in the CD.

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The Multi-Body Gravitational Problem,Deducing the motion of bodies interacting gravitationally is probably the most important mechanical problem but also the most difficult. The threebody problem is not integrable, even if the masses are very small but of comparable size, and this fact prevents in general the use of perturbative methods.

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https://doi.org/10.1007/978-3-658-37294-1nd compared with the “true” motion, obtained from numerical integration. Moreover, the geography of the resonances will be detected thanks to the tools described in the next chapter, which again require a numerical integration.

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