Tensor calculus> definition of contravariants

  • Thread starter Abolaban
  • Start date
  • #1
13
0
Hello Big minds,

In the book of Arfken [Math Meth for Physicists] p 134 he defined contravariant tensor...my question is about a_ij he defined them first as cosines of an angle of basis then he suddenly replaced them by differential notation...why is that?

cosines are not mention in this article as well:
http://en.wikipedia.org/wiki/Covariant_transformation


please note that I newly "ride on my horse" through tensor analysis!


best regards


Abolaban
 

Answers and Replies

  • #2
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
16,829
6,652
General coordinate transformations are not necessarily rotations. When you deal with Cartesian tensors, you will only come across rotations and so your transformations will contain sines and cosines. However, the general case is more ... well ... general.

When you refer to pages in Arfken, please also state the edition - there are now seven of them ...
 
  • #4
13
0
upload_2015-1-30_19-2-24.png


that was from Arfken's book 6th ed
 
  • #5
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
16,829
6,652
Yes, they are compatible. The difference is that Arfken's definition is a more pragmatic one based on the important physics properties of tensors while the other would satisfy a mathematician to a higher degree.
 

Related Threads on Tensor calculus> definition of contravariants

  • Last Post
Replies
8
Views
925
Replies
5
Views
3K
Replies
12
Views
3K
  • Last Post
Replies
7
Views
28K
Replies
8
Views
1K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
7
Views
4K
Top