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A Family of Integrable Perturbed Kepler Systems

Abstract

In the framework of the Poisson geometry of twistor space we consider a family of perturbed 3-dimensional Kepler systems. We show that Hamilton equations of these systems can be integrated in quadratures. Their solutions for some subcases are given explicitly in terms of Jacobi elliptic functions.

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Correspondence to A. Odzijewicz, A. Sliżewska or E. Wawreniuk.

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To the memory of Mikhail Karasev

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Odzijewicz, A., Sliżewska, A. & Wawreniuk, E. A Family of Integrable Perturbed Kepler Systems. Russ. J. Math. Phys. 26, 368–383 (2019). https://doi.org/10.1134/S1061920819030117

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  • DOI: https://doi.org/10.1134/S1061920819030117