A Basic Operations of Tensor Algebra - Springer

← Back to document page

A Basic Operations of Tensor AlgebraThe Tensor calculus is a powerful tool for the description of the fundamentals in con-tinuum mechanics and the derivation of the governing equations for applied prob-lems. In general, there are two possibilities for the representation of the tensors andthe tensorial equations: the direct (symbolic, coordinate-free) notation and the index (component) notationThe direct notation operates with scalars, vectors and tensors as physical objectsdefined in the three-dimensional space (in this book we are limit ourselves to thiscase). A vector (first rank Tensor )aaais considered as a directed line segment ratherthan a triple of numbers (coordinates). A second rank tensorAAAis any finite sumof ordered vector pairsAAA=a ba ba b+...+c dc dc d. The scalars, vectors and tensorsare handled as invariant (independent from the choice of the coordinate system)quantities.

A Basic Operations of Tensor Algebra The tensor calculus is a powerful tool for the description of the fundamentals in con-tinuum mechanics and the derivation of the governing equations for applied prob-lems. In general, there are two possibilities for the representation of the tensors and the tensorial equations:

  Basics, Algebra