An asymmetrical body: example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect
Exactly Solvable and Integrable Systems
2024-08-09 v4 Earth and Planetary Astrophysics
Mathematical Physics
math.MP
Classical Physics
Abstract
We solved the Poisson equations, obtaining their exact solution in elementary functions for the rotation matrix of a free asymmetrical body with angular velocity vector lying on separatrices. This allows us to discuss the temporal evolution of Dzhanibekov's nut directly in the Laboratory system, where it is observed. The rotation matrix depends on two parameters with clear physical interpretation as a frequency and a damping factor of the solution. Qualitative analysis of the solution shows that it properly describes a single-jump Dzhanibekov effect.
Keywords
Cite
@article{arxiv.2401.11518,
title = {An asymmetrical body: example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect},
author = {Alexei A. Deriglazov},
journal= {arXiv preprint arXiv:2401.11518},
year = {2024}
}
Comments
8 pages, matches with published version