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

José Natário | Zendy

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

Author(s) -

José Natário

Publication year - 2010

Publication title -

the journal of geometric mechanics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.511

H-Index - 17

eISSN - 1941-4897

pISSN - 1941-4889

DOI - 10.3934/jgm.2010.2.113

Subject(s) - holonomy , euler's formula , parallel transport , interpretation (philosophy) , geometric phase , phase (matter) , point (geometry) , euler number (physics) , mathematics , motion (physics) , euler equations , mathematical analysis , semi implicit euler method , geometry , physics , classical mechanics , backward euler method , computer science , quantum mechanics , programming language

We give an elementary derivation of the Montgomery phase formula for themotion of an Euler top, using only basic facts about the Euler equation andparallel transport on the 2-sphere (whose holonomy is seen to be responsiblefor the geometric phase). We also give an approximate geometric interpretationof the geometric phase for motions starting close to an unstable equilibriumpoint.

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