## 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

**Download:** **PDF**

### Submission history

[v1] 2012-04-09 16:28:42

[v2] 2012-05-29 12:11:44

[v3] 2015-03-31 14:50:37

**Unique-IP document downloads:** 271 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*