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Published August 1977 | public
Journal Article

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

Abstract

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.

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.

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023