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arXiv · 0909.2109

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

Jose Natario
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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.

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Jose Natario. 2011-10-03. An elementary derivation of the Montgomery phase formula for the Euler top. https://arxiv.org/abs/0909.2109

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