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

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posted on 29.11.2018 by Jinrong Bao, Anatoly Neishtadt
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

SIAM Journal on Applied Dynamical Systems

Citation

BAO, J. and NEISHTADT, A., 2019. Separatrix crossing in rotation of a body with changing geometry of masses. SIAM Journal on Applied Dynamical Systems, 18 (1), pp.150–171.

Publisher

© Society for Industrial and Applied Mathematics (SIAM)

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

26/11/2018

Publication date

2019-01-17

Notes

First Published in SIAM Journal on Applied Dynamical Systems in 18 (1), published by the Society for Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

ISSN

1536-0040

Language

en

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