# Describing Electronic orbit in 3D space using A matrix.

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.

## Answers and Replies

Both

Nugatory
Mentor
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?

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.

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!