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Published 1987 | public
Journal Article

Variational principles on principal fiber bundles: A geometry theory of Clebsch potentials and Lin constraints

Abstract

The geometric theory of Lin constraints and variational principles in terms of Clebsch variables proposed recently by Cendra and Marsden [1987] will be generalized to include those systems defined not only on configuration spaces which are products of Lie groups and vector spaces but on configuration spaces which are principal bundles with structural group G. This generalization includes, for example, fluids with free boundaries, Yang-Mills fields, and it will be very useful, as it will be shown later, to illustrate some aspects of the theory of particles moving in a Yang-Mills field in both its variational and Hamiltonian aspects.

Additional Information

© 1987 Elsevier. Received 23 August 1987. Available online 8 August 2002. Manuscript received; August 23,1987. Research partially supported by NSF Contract DMS 87 - 02502.

Additional details

Created:
August 22, 2023
Modified:
October 20, 2023