Marsden, J. and Montgomery, Sean M. and Ratiu, T. (1989) Cartan-Hannay-Berry Phases and Symmetry. In: Dynamics and Control of Multibody Systems. Contemporary Mathematics, 97 . American Mathematical Society , Providence, R.I., pp. 279-295. ISBN 0821851047 http://resolver.caltech.edu/CaltechAUTHORS:20100902-080916253
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We give a systematic treatment of the treatment of the classical Hannay-Berry phases for mechanical systems in terms of the holonomy of naturally constructed connections on bundles associated to the system. We make the costructions using symmetry and reduction and, for moving systems, we use the Cartan connection. These ideas are woven with the idea of Montgomery  on the averaging of connections to produce the Hannay-Berry connection.
|Item Type:||Book Section|
|Additional Information:||© 1989 American Mathematical Society. Dedicated to Roger Brockett on the occasion of his 50th birthday. Research partially supportcd by NSF grant DMS 8702502, DOE Contract DE-AT03-88ER-12097 and MSI at Cornell University. Research partially supported by an NSF postdoctoral fellowship and NSF grant DMS 8702502. Research partially supported by NSF grant DMS 8701318-01.|
|Classification Code:||AMS Subject Classification 58F, 70H.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||04 Sep 2010 03:29|
|Last Modified:||26 Dec 2012 12:23|
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