An elementary derivation of the Montgomery phase formula for the Euler top

Details An elementary derivation of the Montgomery phase formula for the Euler top An elementary derivation of the Montgomery phase formula for the Euler top

2009-09-11

arxiv.org/abs/0909.2109v3

J. Geom. Mech. 2 (2010) 113-118

Mathematics

Dynamical Systems

6 pages, 2 figures; v2: typos corrected; v3: footnote 6 improved

Scientific paper

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.

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