Reduction, Symmetry And Phases In Mechanics (memoirs Of The American Mathematical Society)

J.e. Marsden, R. Montgomery, And T. Ratiu. Volume 88, Number 436 (first Of 2 Numbers). Includes Bibliographical References (p. ). 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