SamplePublisher`GrassmannCalculus`DifferentialGeometry`
DOrbitFunction  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set the GrassmannPlane.
In[2]:=
SetActiveAssociation
"Grassmann Plane"
[x0,y0,t]
 | PublicGrassmannAtlas |
 | ★★S |
Use a vector field and calculate orbits through a generic point .
(x+3y)+(x-y)
e
x
e
y
★+x0+y0
e
x
e
y
In[3]:=
step1=
[(x+3y)+(x-y),★+x0+y0,t]
| DOrbitFunction |
e
x
e
y
e
x
e
y
Out[3]=
★+(x0+3x0-3y0+3y0)+(-x0+x0+3y0+y0)
1
4
-2t
4t
4t
e
x
1
4
-2t
4t
4t
e
y
We could write a function that might be used in plotting as:
In[4]:=
orbitFunction[x0_,y0_][t_]=step1//
| ToListCoordinates |
Out[4]=
(x0+3x0+3(-1+)y0),((-1+)x0+(3+)y0)
1
4
-2t
4t
4t
1
4
-2t
4t
4t
A specific orbit that goes through would be:
{1,1}
In[5]:=
orbitFunction[1,1][t]//Simplify
Out[5]=
(-1+3),(1+)
1
2
-2t
4t
1
2
-2t
4t
The position on the orbit at parameter value would be:
0.5
In[6]:=
orbitFunction[1,1][0.5]
Out[6]=
{3.89348,1.54308}
In[7]:=
Clear[step1,orbitFunction]
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""