2019/01/13 by Len Bos, Bos, Len, Michael A. Slawinski +5
Physics and Astronomy · #FOS: Physical sciences #Geophysics (physics.geo-ph) #physics.geo-ph
paper · pdf · doi:10.48550/arxiv.1901.03926
arxiv created 2019/01/13 · arxiv updated 2019/01/15
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 R3, 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.