Exact Description of Rotational Waves in an Elastic Solid

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.

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Acknowledgment

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

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Correspondence to R. A. Close.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Close, R.A. Exact Description of Rotational Waves in an Elastic Solid. Adv. Appl. Clifford Algebras 21, 273–281 (2011). https://doi.org/10.1007/s00006-010-0249-1

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Mathematics Subject Classification (2010)

  • 74B05
  • 81P10

Keywords

  • Elastic solid
  • rotational waves
  • transverse waves
  • Dirac equation