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Some applications of geometry is continuum mechanics^(*1)

Hughes, Thomas J. R. and Marsden, Jerrold E. (1977) Some applications of geometry is continuum mechanics^(*1). Reports on Mathematical Physics, 12 (1). pp. 35-44. ISSN 0034-4877. doi:10.1016/0034-4877(77)90044-1.

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Some contemporary ideas from differential geometry are applied to continuum mechanics. The Lie derivative is used to clarify the notion of “objective rates”, an intrinsic treatment of Piola transformations is described, a simplified proof of Vainberg's theorem for potential operators is given by way of the Poincaré lemma on infinite dimensional manifolds, and a new derivation of the basic equations of continuum mechanics is presented which is valid in a general Riemannian manifold setting.

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Additional Information:© 1977 Published by Elsevier Science Ltd. All rights reserved. Received 11 September 1976. Available online 28 March 2002. Partially supported by the National Science Foundation. Prepared for the symposium on methods of differential geometry in physics and mechanics, June 1976, Warsaw.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19475
Deposited By: Ruth Sustaita
Deposited On:17 Aug 2010 21:54
Last Modified:08 Nov 2021 23:52

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