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arXiv · 1901.03926

On orthogonal transformations of Christoffel equations

Len Bos·Michael A. Slawinski·Theodore Stanoev·Maurizio Vianello
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Abstract

The purpose of this paper is to prove the equivalence$-$under rotations of distinct terms$-$of different forms of a determinantal equation that appears in the studies of wave propagation in Hookean solids, in the context of the Christoffel equations. To do so, we prove a general proposition that is not limited to ${\mathbb R}^3$, nor is it limited to the elasticity tensor with its index symmetries. Furthermore, the proposition is valid for orthogonal transformations, not only for rotations. The sought equivalence is a corollary of that proposition.

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Len Bos, Michael A. Slawinski, Theodore Stanoev, Maurizio Vianello. 2019-01-13. On orthogonal transformations of Christoffel equations. https://arxiv.org/abs/1901.03926

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