March  2010, 2(1): 113-118. doi: 10.3934/jgm.2010.2.113

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

1. 

Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal

Received  September 2009 Revised  February 2010 Published  April 2010

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.
Citation: José Natário. An elementary derivation of the Montgomery phase formula for the Euler top. Journal of Geometric Mechanics, 2010, 2 (1) : 113-118. doi: 10.3934/jgm.2010.2.113
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