SamplePublisher`GrassmannCalculus`
GrassmannGrad  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set Cartesian coordinates.
In[2]:=
 | SetCoordinateVectorSpace |
Gradient of a function.
In[3]:=
| GrassmannGrad |
2
x
Out[3]=
2xyz+z+y
e
x
2
x
e
y
2
x
e
z
Gradient of a radial distance from the origin.
In[4]:=
| GrassmannGrad |
2
x
2
y
2
z
Out[4]=
x
e
x
2
x
2
y
2
z
y
e
y
2
x
2
y
2
z
z
e
z
2
x
2
y
2
z
The gravitational force the gradient of a potential.
1/r
In[5]:=
 | GrassmannGrad |
2
x
2
y
2
z
Out[5]=
-x-y-z
e
x
e
y
e
z
3/2
(++)
2
x
2
y
2
z
In spherical coordinates:
In[6]:=
| SetActiveSpacePreferences |
| PublicGrassmannAtlas |
In[7]:=
| GrassmannGrad |
Out[7]=
-
e
r
2
r
In cylindrical coordinates we see why a cloud of particles rotating about the ζ axis will collapse to a disk:
In[8]:=
| SetActiveSpacePreferences |
| PublicGrassmannAtlas |
In[9]:=
| GrassmannGrad |
2
ρ
2
ζ
Out[9]=
--
ζ
e
ζ
3/2
(+)
2
ζ
2
ρ
ρ
e
ρ
3/2
(+)
2
ζ
2
ρ
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