文档介绍：TENSOR ANALYSIS
with applications to
Geometry and Continuum Mechanics
C J Camilleri
ponents of Tensor Derivatives
X n o
g
1 ∂˜b ˜b ∂h h h
∇ b = ik + ik I K − L l ˜b
m ik h ∂um h h h ∂um h h im lk
f M I K M I M
g
˜
δbik . . . (u, t) ∂bik . . .
= +v ˜m∇mbik . . . ,m
g δt ∂t X
g
˜
Dbik . . . (u, t) ∂bik . . . ˜
= +v ˜m∇mbik . . . + ω˜imbmk . . .
f Dt g∂t X X
Vb . . k . . (u, t) Db
. i . . . . ik . . ˜ 0 ˜
= + e˜mib . mk . . − e˜kmb . im . .
g Vt g Dt
£b . k =v ˜∇ b +ω˜˜b +ω˜˜b +e ˜˜b − e˜˜b
v i m m ik im mk km im im mk km im Curvilinear Coordinates
Summation is understood over repeated lower-case indices. ponents or summation are implied
P
by upper-case suffixes of the scale factors – they are just labels. At each stage an upper-case suffix
‘follows’ the value of the corresponding lower-case index. The denotes the sum of all such terms, one
for each similar index of the tensor.
Electronic
Portable Document Format (PDF)
copy to
M J Roberts
of
Portsmouth, England
With best wishes
TENSOR ANALYSIS
with applications to
Geometry and Continuum Mechanics
C J Camilleri
Department of Mathematics
University of Malta
Second Edition
July 16, 2004
First Edition published in 1999 by
Malta University Press, Tal-Qroqq, Msida, Malta
Second Edition in electronic-pdf format published in 2004 by
C J Camilleri, Department of Mathematics
University of Malta, Tal-Qroqq, Msida, Malta
Typesetting and Page Layout Produced C J Camilleri.
All rights reserved. No part of this publication may be reproduced,
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without the prior permission of the author.
Copyright ­c C J Camilleri 1999 and 2004.
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