Separatrix crossing in rotation of a body with changing geometry of masses

Jinrong Bao; Anatoly Neishtadt

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arXiv · 1712.05357

Separatrix crossing in rotation of a body with changing geometry of masses

Jinrong Bao·Anatoly Neishtadt

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Abstract

We consider free rotation of a body whose parts move slowly with respect to each other under the action of internal forces. This problem can be considered as a perturbation of the Euler-Poinsot problem. The dynamics has an approximate conservation law - an adiabatic invariant. This allows to describe the evolution of rotation in the adiabatic approximation. The evolution leads to an overturn in the rotation of the body: the vector of angular velocity crosses the separatrix of the Euler-Poinsot problem. This crossing leads to a quasi-random scattering in body's dynamics. We obtain formulas for probabilities of capture into different domains in the phase space at separatrix crossings.

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BibTeX RIS

Jinrong Bao, Anatoly Neishtadt. 2017-12-14. Separatrix crossing in rotation of a body with changing geometry of masses. https://arxiv.org/abs/1712.05357

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