On Some Applications of the Absolute Differential Calculus to Physics
Abstract
By means of the tensor analysis, coupled with the first fundamental theorem on the invariants of orthogonal transformations, expressions, independent of the particular type of coordinates used are derived for Hooke's law in elasticity theory and for the constitutive relations in electromagnetic theory. It is shown that these two laws are but special cases of a more general physical law connecting, in a linear way, the components of two tensors having physical significance. It is to be noted that in the case of Hooke's law for a transversely isotropic medium, six independent coefficients of elasticity are involved instead of five found in the corresponding classical expressions.
- Publication:
-
Physical Review
- Pub Date:
- January 1933
- DOI:
- 10.1103/PhysRev.43.137
- Bibcode:
- 1933PhRv...43..137K