SamplePublisher`GrassmannCalculus`
GrassmannMaterialDerivative  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetCoordinateVectorSpace |
In[3]:=
vectorA=y-x+Sin[y]vectorB=++
[vectorA,vectorB]
e
x
e
y
e
z
2
x
e
x
2
y
e
y
2
z
e
z
| GrassmannMaterialDerivative |
Out[3]=
y-x+Sin[y]
e
x
e
y
e
z
Out[3]=
2
x
e
x
2
y
e
y
2
z
e
z
Out[3]=
2xy-2xy+2zSin[y]
e
x
e
y
e
z
It appears that the material derivative applied to the position vector always returns the A vector.
In[4]:=
vectorA=
[]+yz++zx/.
vectorB=x+y+z
[vectorA,vectorB]%vectorA//Simplify
 | RandomGrassmannVector |
e
x
2
x
e
y
e
z
 | VectorToOrthonormal |
e
x
e
y
e
z
| GrassmannMaterialDerivative |
Out[4]=
-9+yz-9++3+xz
e
x
e
x
e
y
2
x
e
y
e
z
e
z
Out[4]=
x+y+z
e
x
e
y
e
z
Out[4]=
(-9+yz)+(-9+)+(3+xz)
e
x
2
x
e
y
e
z
Out[4]=
True
In[5]:=
| SetActiveSpacePreferences |
| PublicGrassmannAtlas |
In[6]:=
vectorA=
[]++r+Sin[θ]Cos[φ]/.
vectorB=r
[vectorA,vectorB]%vectorA//Simplify
| RandomGrassmannVector |
2
r
e
r
2
Sin[θ]
e
θ
e
φ
| VectorToOrthonormal |
e
r
| GrassmannMaterialDerivative |
Out[6]=
-6++3r+7rSin[θ]++rCos[φ]
e
r
2
r
e
r
e
θ
e
φ
2
r
e
θ
2
Sin[θ]
e
φ
2
Sin[θ]
Out[6]=
r
e
r
Out[6]=
(-6+)+rSin[θ](7+Cos[φ]Sin[θ])+r(3+r)
2
r
e
r
e
φ
e
θ
2
Sin[θ]
Out[6]=
True
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""