Tensor Analysis Schaum Series Pdf 38 [work] Page

(at bottom of page) – often problems asking the reader to:

A crucial solved problem on page 38 demonstrates that any second-rank tensor ( T_ij ) can be decomposed: [ T_ij = \frac12(T_ij + T_ji) + \frac12(T_ij - T_ji) = S_ij + A_ij ] Where ( S_ij ) is symmetric and ( A_ij ) is antisymmetric. The solution shows that the contraction of a symmetric tensor with an antisymmetric tensor is zero—a result used repeatedly in continuum mechanics to simplify stress-energy equations. Tensor Analysis Schaum Series Pdf 38