We 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 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.
On orthogonal transformations of the Christoffel equations
Vianello M.
2020-01-01
Abstract
We 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 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.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Bos2020_Article_OnOrthogonalTransformationsOfT.pdf
Accesso riservato
Descrizione: Articolo principale
:
Publisher’s version
Dimensione
200.34 kB
Formato
Adobe PDF
|
200.34 kB | Adobe PDF | Visualizza/Apri |
|
11311-1165886_Vianello.pdf
accesso aperto
:
Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione
82.85 kB
Formato
Adobe PDF
|
82.85 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
