Advanced Strength and Applied Elasticity, Fourth Edition

Appendix A Indicial Notation

A particular class of tensor, a vector, requires only a single subscript to describe each of its components. Often the components of a tensor require more than a single subscript for definition. For example, second-order or second-rank tensors, such as those of stress or inertia, require double subscripting: τ_ij, I_ij. Quantities such as temperature and mass are scalars, classified as tensors of zero rank.

Tensor or indicial notation, here briefly explored, offers the advantage of succinct representation of lengthy equations through the minimization of symbols. In addition, physical laws expressed in tensor form are independent of the choice of coordinate system, and therefore similarities in seemingly different physical ...