An asymmetrical body: example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect

Author:

Alexei A. Deriglazov

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph)

journal:

date:

2024-01-21 00:00:00

Abstract

We solve the Poisson equations and present an 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 describe a one-jump Dzhanibekov effect.

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