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

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.

8 pages, matches with published version

References in corpus (3)

• Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system
• Analytical solution of the Euler-Poinsot problem
• Euler-Poisson equations of a dancing spinning top, integrability and examples of analytical solutions

Cited by in corpus (2)

• General solution to Euler-Poisson equations of a free symmetric body by direct summation of power series
• An alternative interpretation of the Grioli gyroscope suspension points