Bifurcation analysis of the problem of a "rubber" ellipsoid of revolution rolling on a plane
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909575864647680 |
|---|---|
| author | Kilin, Alexander Pivovarova, Elena |
| author_facet | Kilin, Alexander Pivovarova, Elena |
| contents | This paper is concerned with the problem of an ellipsoid of revolution rolling on a horizontal plane under the assumption that there is no slipping at the point of contact and no spinning about the vertical. A reduction of the equations of motion to a fixed level set of first integrals is performed. Permanent rotations corresponding to the rolling of an ellipsoid in a circle or in a straight line are found. A linear stability analysis of permanent rotations is carried out. A complete classification of possible trajectories of the reduced system is performed using a bifurcation analysis. A classification of the trajectories of the center of mass of the ellipsoid depending on parameter values and initial conditions is performed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bifurcation analysis of the problem of a "rubber" ellipsoid of revolution rolling on a plane Kilin, Alexander Pivovarova, Elena Dynamical Systems 37J60, 70E18, 70E40, 70E50 This paper is concerned with the problem of an ellipsoid of revolution rolling on a horizontal plane under the assumption that there is no slipping at the point of contact and no spinning about the vertical. A reduction of the equations of motion to a fixed level set of first integrals is performed. Permanent rotations corresponding to the rolling of an ellipsoid in a circle or in a straight line are found. A linear stability analysis of permanent rotations is carried out. A complete classification of possible trajectories of the reduced system is performed using a bifurcation analysis. A classification of the trajectories of the center of mass of the ellipsoid depending on parameter values and initial conditions is performed. |
| title | Bifurcation analysis of the problem of a "rubber" ellipsoid of revolution rolling on a plane |
| topic | Dynamical Systems 37J60, 70E18, 70E40, 70E50 |
| url | https://arxiv.org/abs/2405.07511 |