Rotation Matrix

Discussion in 'Math' started by Key, Apr 13, 2014.

  1. Key

    Thread Starter New Member

    Jun 21, 2013
    14
    2
    Hello everyone, someoneone bad at maths here asking questions about rotation matrices.

    Am I correct to assume in rotation matrix we compare the rotation of coordinate system B to A ? For example in row 1 column 2, we compare the coordinate B X-axis to coordinate system A Y-axis ?
    And the formula on the right is when we rotate the X and Y axis of coordinate system B counterclockwise and we leave axis Z untouched ?
    That is where we get our corner alpha ? and why zaxis value is 1 for parallel and the others are 0 for being crossed ?

    Could someone poke me in the right direction if I am wrong here ?

    And excuse the MSPaint, didnt have anything better at hand.
     
  2. Key

    Thread Starter New Member

    Jun 21, 2013
    14
    2
    if I happen to be right, could someone please explain to me how the sines cosines are gotten, in this more simpler 2 axis coordinate system.

    Thank you
     
  3. MrChips

    Moderator

    Oct 2, 2009
    12,414
    3,353
    Go back to basic trigonometry.
    Start with 2-D rotation.

    Suppose you have a point (x,y) in X-Y Cartesian coordinates.
    What is the position of the point in polar coordinates, (r,θ)?

    x = r cos θ
    y = r sin θ

    Now rotate the X,Y coordinate system by α-degrees in a counter clockwise direction.

    The position (x,y) in the new system is r, (θ-α)
    The new (x,y) coordinates are
    x = r cos(θ - α)
    y = r sin(θ - α)

    Expand these two equations:

    x = r ( cos θ cos α + sin θ sin α )
    y = r ( sin θ cos α - cos θ sin α )

    See if you can come up with the rotational matrix for 2-D rotation.
     
  4. Key

    Thread Starter New Member

    Jun 21, 2013
    14
    2
    why is it θ-α ? why isnt it
    x=r*cos(θ-a)
    y=r*sin(θ+a)
    in your example
    and how does this fit into a matrix ?
    oh man im rly bad at this
     
  5. MrChips

    Moderator

    Oct 2, 2009
    12,414
    3,353
    Sure. Replace α with a. Same thing.
     
Loading...