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Express a vector in a rotated coordinate system

  1. Jul 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Hi

    I have a coordinate system (x', y') and a vector v'=(1, 0) here. There is a different coordinate system (x, y), which is rotated about the y-axis relative to (x', y') by an angle Ω. I am trying to express v' in the system (x, y).

    At first what I tried to do was to rotate v' by an angle Ω around the y-axis by a rotation matrix, but then it occurred to me that this only rotates the vector, it does not express it in the system (x, y). Can I get a hint to how to achieve this?

    Thanks in advance.
     
  2. jcsd
  3. Jul 11, 2013 #2

    HallsofIvy

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    Expressing a vector in a coordinate system that has been rotated by angle [itex]\theta[/itex] is the same as rotating the vector, in the original coordinate system by [itex]-\theta[/itex].

    For example, if I rotate coordinate system x'y' by 90 degrees, counterclock wise, then the new positive x-axis is the old y'-axis and the new positive y-axis is the old negative x'-axis. (1, 0) becomes (0, -1), exactly the same as rotating the vector itself 90 degrees clockwise.
     
  4. Jul 11, 2013 #3
    I see, that makes good sense. Thanks for helping me out these past days.
     
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