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Cartan-Hannay-Berry Phases and Symmetry

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. Vol.97. American Mathematical Society , Providence, R.I., pp. 279-295. ISBN 0821851047. https://resolver.caltech.edu/CaltechAUTHORS:20100902-080916253

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Abstract

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 [1988] on the averaging of connections to produce the Hannay-Berry connection.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://www.ams.org/bookstore?co1=AND&co2=AND&co3=AND&d=BOOK&f=G&fn=105&l=100&op1=ADJ&op2=ADJ&op3=ADJ&p=1&pg1=&pg2=&pg3=ALLF&r=25&s1=&s2=&s3=quantum%20control&subject=genint&u=PublisherArticle
ORCID:
AuthorORCID
Ratiu, T.0000-0003-1972-5768
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.
Funders:
Funding AgencyGrant Number
NSFDMS 8702502
Department of Energy (DOE)DE-AT03-88ER-12097
MSI/Cornell UniversityUNSPECIFIED
NSF Postdoctoral FellowshipUNSPECIFIED
NSFDMS 8702502
NSFDMS 8701318-01
Series Name:Contemporary Mathematics
Classification Code:AMS Subject Classification 58F, 70H.
Record Number:CaltechAUTHORS:20100902-080916253
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100902-080916253
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19763
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:04 Sep 2010 03:29
Last Modified:09 Mar 2020 13:19

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