00065___3a151836381135a86f46c8d469000f79 - shall This...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
44 TENSOR ANALYSIS Chap. 2 etc. The inverse transform is Hence, (4) and the distinction between the transformation laws (2.4:2) and (2.4:4) disappears. The components of a vector in the two coordinate systems are related by %(51,32,33) =,&jvj(xliX2,x3). The components of a tensor of rank two are related by cij(3,32,z3) =Pik@js~ks(Xl,x2,~3). When only rectangular Cartesian coordinates are considered, we
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: shall This convenient practice will be followed write all indices as subscripts. throughout this book. 2.9. CONTRACTION We shall now consider some operations on tensors that generate new Let Aikl be a mixed tensor so that, in a transformation from the coor- tensors. dinates xa to za(a = 1,2,. . . ,n), we obtain _ . a2 ax0 ax7 a d A? (z) = - --- A" l k l ax* 833 a z k 831 P+(x) . If we equate the indices i and k and sum, we obtain the set of quantities...
View Full Document

Ask a homework question - tutors are online