Describing Electronic orbit in 3D space using A matrix.

[kenneththo85431]

I've plotted out the trajectory of an imaginary electron in 3D; next I represent it's points with the matrix A(x1 y1 z1) "throughout it's orbit":
( -1/2 -1 1
( -2 -1.5 2
(-1/2 2 3
( 1 3 1 )
2 -2 -1

Any pointers on where to go from here would be greatly appreciated. External links are helpful too.

 

[kenneththo85431]

Both

 

[Nugatory]

You'll have to tell us more. What are you trying to do here? What problem are you trying to solve? How did you come up with these four positions?

 

[kenneththo85431]

Yes, I'm new to matrices and I am looking for resources to create objects in 3 dimensions then model those objects in 3 dimensions.

 

[Mentz114]

I've plotted out the trajectory of an imaginary electron in 3D; next I represent it's points with the matrix A(x1 y1 z1) "throughout it's orbit":
( -1/2 -1 1
( -2 -1.5 2
(-1/2 2 3
( 1 3 1 )
2 -2 -1

Any pointers on where to go from here would be greatly appreciated. External links are helpful too.

One way to do this is to start with a position vector in the x-y plane $\vec{x}=(x,y)$ and use a 2x2 matrix to change the position by multiplication so that $\vec{x}_{n+1}=M\vec{x}_n$,

For instance
$$M= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }$$
so that
$$M\vec{x}= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }\vec{x}=\pmatrix{\sin\left( a\right) \,y+\cos\left( a\right) \,x\cr \cos\left( a\right) \,y-\sin\left( a\right) \,x}$$
If you start with position (-1,0) and choose a small $a$, say 0.05 radians, then applying the matrix successively moves the point in a circle with radius 1 and center 0.

 

[kenneththo85431]

One way to do this is to start with a position vector in the x-y plane $\vec{x}=(x,y)$ and use a 2x2 matrix to change the position by multiplication so that $\vec{x}_{n+1}=M\vec{x}_n$,

For instance
$$M= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }$$
so that
$$M\vec{x}= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }\vec{x}=\pmatrix{\sin\left( a\right) \,y+\cos\left( a\right) \,x\cr \cos\left( a\right) \,y-\sin\left( a\right) \,x}$$
If you start with position (-1,0) and choose a small $a$, say 0.05 radians, then applying the matrix successively moves the point in a circle with radius 1 and center 0.

Wow! Thank you so much!