An elementary derivation of the Montgomery phase formula for the Euler top
Dynamical Systems
2011-10-04 v3 Mathematical Physics
Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
We give an elementary derivation of the Montgomery phase formula for the motion of an Euler top, using only basic facts about the Euler equation and parallel transport on the 2-sphere (whose holonomy is seen to be responsible for the geometric phase). We also give an approximate geometric interpretation of the geometric phase for motions starting close to an unstable equilibrium point.
Keywords
Cite
@article{arxiv.0909.2109,
title = {An elementary derivation of the Montgomery phase formula for the Euler top},
author = {Jose Natario},
journal= {arXiv preprint arXiv:0909.2109},
year = {2011}
}
Comments
6 pages, 2 figures; v2: typos corrected; v3: footnote 6 improved