An asymmetrical body: example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914904834834432 |
|---|---|
| author | Deriglazov, Alexei A. |
| author_facet | Deriglazov, Alexei A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11518 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An asymmetrical body: example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect Deriglazov, Alexei A. Exactly Solvable and Integrable Systems Earth and Planetary Astrophysics Mathematical Physics Classical Physics 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. |
| title | An asymmetrical body: example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect |
| topic | Exactly Solvable and Integrable Systems Earth and Planetary Astrophysics Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2401.11518 |