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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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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DOI: https://doi.org/10.1007/s00006-010-0249-1