- #1

- 4

- 0

( -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.

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- Thread starter kenneththo85431
- Start date

- #1

- 4

- 0

( -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.

- #2

- 4

- 0

Both

- #3

Nugatory

Mentor

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- #4

- 4

- 0

- #5

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- 292

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##,

( -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.

For instance

[tex]

M= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }

[/tex]

so that

[tex]

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}

[/tex]

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.

- #6

- 4

- 0

Wow! Thank you so much!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

[tex]

M= \pmatrix{\cos\left( a\right) & \sin\left( a\right) \cr -\sin\left( a\right) & \cos\left( a\right) }

[/tex]

so that

[tex]

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}

[/tex]

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.

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