张量分析.ppt

文档介绍：1, , applications of tensor analysis, dover publications,Inc , NEW York
2, Garl , handbook of applied mathematics, Van Nostrand Reinhold ; 2nd edition
3, . sokolnikoff, tensor analysis, Walter de Gruyter ; 2Rev Ed edition
4. , introduction to vectors and tensor analysis, Dover Publications ; New Ed edition
Flugge, tensor analysis and continuum mechanics , Springer ; 1 edition
, vector and tensor analysis, CRC ; 2 edition
7. 黃克智,薛明德,陸明萬, 張量分析, 北京清華大學出版社
Tensor analysis
1、Vector in Euclidean 3-D
2、Tensors in Euclidean 3-D
3、general curvilinear coordinates in Euclidean 3-D
4、tensor calculus
1-1 Orthonormal base vector:
Let (e1,e2,e3) be a right-handed
set of three mutually perpendicular
vector of unit magnitude
1、Vector in euclidean 3-D
ei (i = 1,2,3)may be used to define the kronecker delta δij and the permutation symbol eijk by means of the equations
and
[prove]
By setting r= i we recover the e –δ relation
Thus δij = 1 for i=j ; e123 =e312=e231=1;e132=e321=e213=-1;
All other eijk = 0. in turn,a pair of eijk is related to a determinate of δij by
(1-1-1)
Rotated set of orthonormal base vector is introduced. the corresponding ponents of F may puted in terms of the old ones by writing
We have transformation rule
Here
1-2 ponent of vectors transformation rule
These direction cosines satisfy the useful relations
(1-2-1)
[prove]
1-3 General base vectors:
ponents with respect to a triad of base vector need not be resticted to the use of orthonomal vector .let ε1, ε2 , ε3 be any three noncoplanar vector that play the roles of general base vectors
and
(metric tensor)
(permutation tensor)
From (1-1-1) the general vector identity
can be established
(*)