The Main Paradox of Kam-Theory for Restricted Three-Body Problem (R3BP, Celestial Mechanics)

Authors: Sergey V. Ershkov

Here are presented a key points of criticism of KAM (Kolmogorov-Arnold-Moser) theory in the application of main results to the field of celestial mechanics, especially in the case of restricted three-body problem. The main paradox of KAM-theory is that an appropriate Hamilton formalism should be valid for the KAM dynamical systems, but Hamilton formalism could not be applied for restricted three-body problem (which is proved to have only the Jacobian-type integral of motion, but the integrals of energy, momentum are not invariants). Besides, we should especially note that there is no analogue of Jacobian-type integral of motion in the case of photogravitational restricted three-bodt problem if we take into consideration even a negligible Yarkovsky effect.

Comments: 8 Pages. Key Words: KAM (Kolmogorov-Arnold-Moser) theory, Hamilton formalism, Yarkovsky effect, photogravitational restricted three-body problem, Jacobian-type integral of motion

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Submission history

[v1] 2012-04-09 16:28:42
[v2] 2012-05-29 12:11:44
[v3] 2015-03-31 14:50:37

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