Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
BowenPing`STensor`
SCoordinateTransform  |
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Details and Options
Examples
(3)
Basic Examples
(2)
Create some tensor in 3D Euclidean space in Cartesian Coordinates first:
In[1]:=
car3={x,y,z};sph3={r,θ,ϕ};g=
"g",{0,2},car3,IdentityMatrix[3],
True;T=
["T",{1,0},car3,{1,0,0}];
 | CreateTensor |
 | IsMetric |
| CreateTensor |
If we want to transform from Cartesian Coordinates to Spherical Coordinates in 3D Euclidean space, we can use to get transformation:
In[2]:=
ts=CoordinateTransformData["Cartesian""Spherical","Mapping"];invts=CoordinateTransformData["Spherical""Cartesian","Mapping"];
ts and invts are both pure functions, remember that.
In[3]:=
 | SCoordinateTransform |
Out[3]=
STensor
 |  |
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We can get the components, and simply them by Spherical Coordinates conditions:
In[4]:=
Simplify
[T,sph3,ts,invts]["Components"],r>0&&0≤θ<Pi//MatrixForm
| SCoordinateTransform |
Out[4]//MatrixForm=
Cos[ϕ]Sin[θ] |
Cos[θ]Cos[ϕ] r |
- Csc[θ]Sin[ϕ] r |
In[5]:=
Simplify
[g,sph3,ts,invts]["Components"],r>0&&0≤θ<Pi//MatrixForm
| SCoordinateTransform |
Out[5]//MatrixForm=
1 | 0 | 0 |
0 | 2 r | 0 |
0 | 0 | 2 r 2 Sin[θ] |
If the transformation has been recorded in with names, you can directly use them as input:
In[1]:=
Simplify
[T,sph3,"Cartesian""Spherical"]["Components"],r>0&&0≤θ<Pi//MatrixForm
| SCoordinateTransform |
Out[1]//MatrixForm=
Cos[ϕ]Sin[θ] |
Cos[θ]Cos[ϕ] r |
- Csc[θ]Sin[ϕ] r |
And Hyperspherical includes 3D spherical, the dimension is determined by the dimension of coordinate system:
In[2]:=
Simplify
[g,sph3,"Cartesian""Hyperspherical"]["Components"],r>0&&0≤θ<Pi//MatrixForm
| SCoordinateTransform |
Out[2]//MatrixForm=
1 | 0 | 0 |
0 | 2 r | 0 |
0 | 0 | 2 r 2 Sin[θ] |
Neat Examples
(1)
""