Reduction, Symmetry, and Phases in Mechanics

Download or read book Reduction, Symmetry, and Phases in Mechanics written by Jerrold E. Marsden and published by American Mathematical Soc.. This book was released on 1990 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.