English

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