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Advances in Applied Clifford Algebras

, Volume 21, Issue 2, pp 273–281 | Cite as

Exact Description of Rotational Waves in an Elastic Solid

  • R. A. CloseEmail author
Open Access
Article

Abstract

Conventional descriptions of transverse waves in an elastic solid are limited by an assumption of infinitesimally small gradients of rotation. By assuming a linear response to variations in orientation, we derive an exact description of a restricted class of rotational waves in an ideal isotropic elastic solid. The result is a nonlinear equation expressed in terms of Dirac bispinors. This result provides a simple classical interpretation of relativistic quantum mechanical dynamics.We construct a Lagrangian of the form \({\fancyscript{L} = -\fancyscript{E} + U + K = 0}\), where \({\fancyscript{E}}\) is the total energy, U is the potential energy, and K is the kinetic energy.

Mathematics Subject Classification (2010)

74B05 81P10 

Keywords

Elastic solid rotational waves transverse waves Dirac equation 

Notes

Acknowledgment

The author is grateful to Damon Merari for his interest and encouragement.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.PortlandUSA

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