Reduction, Symmetry, and Phases in Mechanics
jan. 1990 · American Mathematical Society: Memoirs of the American Mathematical Society 436. knjiga · American Mathematical Soc.
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Various holonomy phenomena are shown to be instances of the reconstruction procedure for mechanical systems with symmetry. We systematically exploit this point of view for fixed systems and for slowly moving systems in adiabatic context. For the latter, we obtain the phases as the holonomy for a connection which synthesizes the Cartan connection for moving mechanical systems with the Hannay-Berry connection for integrable systems.
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