Stability of symmetric tops via one variable calculus
| dc.creator | Lerman, Eugene | |
| dc.date | 1996-08-28 | |
| dc.date.accessioned | 2026-07-07T09:12:51Z | |
| dc.date.available | 2026-07-07T09:12:51Z | |
| dc.description | We study the stability of symmetric trajectories of a particle on the Lie group $SO(3)$ whose motion is governed by an $SO(3)\times SO(2)$ invariant metric and an $SO(2)\times SO(2)$ invariant potential. Our method is to reduce the number of degrees of freedom at {\em singular} values of the $SO(2)\times SO(2)$ momentum map and study the stability of the equilibria of the reduced systems as a function of spin. The result is an elementary analysis of the fast/slow transition in the Lagrange and Kirchhoff tops. More generally, since an $SO(2)\times SO(2)$ invariant potential on $SO(3)$ can be thought of as ${\bf Z}_2$ invariant function on a circle, we get a condition on the second and fourth derivatives of the potential at the symmetric points that guarantees that the corresponding system gains stability as the spin increases. | |
| dc.description | 10 pages, LaTeX, uses epic and eepic style files | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9608010 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9608010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152161 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58F | |
| dc.title | Stability of symmetric tops via one variable calculus | |
| dc.type | text |