Basic Examples (4)
Basic Examples
(4)
Transform a covariant rank-2 tensor in a cylindrical coordinate system to its contravariant form :
t
ij
ij
t
In[1]:=
8Sin[2ϕ] | 1 2 | 3Cos[ϕ] |
1 2 | 11 2 2 r | r8Cos[ϕ] |
5Cos[ϕ] | 5rSin[ϕ] | 2 |
1 | 0 | 0 |
0 | 2 r | 0 |
0 | 0 | 1 |
Out[1]//MatrixForm=
8Sin[2ϕ] | Cos[2ϕ] 2r | 3Cos[ϕ] |
1 2r | 11 2 2 r | 8Cos[ϕ] r |
5Cos[ϕ] | 5Sin[ϕ] r | 2 |
———
Transform a covariant rank-2 tensor in cylindrical coordinates to its mixed form :
t
ij
i
t
j
In[1]:=
8Sin[2ϕ] | 1 2 | 3Cos[ϕ] |
1 2 | 11 2 2 r | r8Cos[ϕ] |
5Cos[ϕ] | 5rSin[ϕ] | 2 |
1 | 0 | 0 |
0 | 2 r | 0 |
0 | 0 | 1 |
Out[2]//MatrixForm=
8Sin[2ϕ] | Cos[2ϕ] 2r | 3Cos[ϕ] |
r 2 | 11 2 | 8rCos[ϕ] |
5Cos[ϕ] | 5Sin[ϕ] r | 2 |
———
Convert for a :
t
ij
ij
t
In[1]:=
σ
11
σ
12
σ
22
Out[1]=
StructuredArray
———
Attempting the conversion changes nothing:
ij
t
ij
t
In[1]:=
8Sin[2ϕ] | 1 2 | 3Cos[ϕ] |
1 2 | 11 2 2 r | r8Cos[ϕ] |
5Cos[ϕ] | 5rSin[ϕ] | 2 |
1 | 0 | 0 |
0 | 2 r | 0 |
0 | 0 | 1 |
Out[4]//MatrixForm=
8Sin[2ϕ] | 1 2 | 3Cos[ϕ] |
r 2 | 11 2 r 2 | 8rCos[ϕ] |
5Cos[ϕ] | 5rSin[ϕ] | 2 |
Scope (17)
Scope
(17)
Properties & Relations (1)
Properties & Relations
(1)