00065___3a151836381135a86f46c8d469000f79

00065___3a151836381135a86f46c8d469000f79 - shall This...

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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
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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...
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