How to Calculate a 3x3 Rotation Matrix around a Given Axis?

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Discussion Overview

The discussion revolves around calculating a 3x3 rotation matrix that represents a rotation of Pi/6 around a specified axis defined by the vector v = {1, 2, 3}. The focus includes both the mathematical formulation and the interpretation of the axis and direction of rotation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks guidance on deriving the rotation matrix for a specific angle and axis.
  • Another participant clarifies the definition of the axis of rotation and inquires about the direction of rotation (clockwise or counterclockwise).
  • A later reply suggests determining the results of rotating standard basis vectors as a preliminary step in constructing the matrix.
  • Additional posts provide links to external resources that may offer further information on rotation matrices.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the direction of rotation, and the discussion includes multiple viewpoints regarding the approach to calculating the rotation matrix.

Contextual Notes

There is uncertainty regarding the direction of rotation, which may affect the final matrix. The discussion does not fully resolve the mathematical steps involved in deriving the rotation matrix.

yanyin
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Hi, if i want to find a 3x3 matrix R which represents a rotation of Pi/6 around the axis of rotation v(vector)={1, 2, 3}. how can i find it?
 
Last edited:
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Are you saying that your axis is along a vector that starts at the origin of the coordinate system and has its tip at the point (x,y,z)=(1,2,3)? And is your rotation direction clockwise or counterclockwise as viewed from the perspective of (0,0,0)?
 
Originally posted by Janitor
Are you saying that your axis is along a vector that starts at the origin of the coordinate system and has its tip at the point (x,y,z)=(1,2,3)? And is your rotation direction clockwise or counterclockwise as viewed from the perspective of (0,0,0)?
Thanks. it's a vector from origin to (1, 2, 3). which direction? i am not sure yet. let say clockwise.
 
Start by figuring out what the result of rotating
[0,0,1]
[0,1,0]
and
[1,0,0]
are.

Once you've done that, you shouldn't have any trouble making hte matrix.
 

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