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2D Rotation Matrix

  1. Feb 13, 2014 #1
    I was trying to deduce the 2D Rotation Matrix and I got frustrated. So, I found this article: Ampliación del Sólido Rígido/ (in Spanish).

    rotacic3b3n-vectores.jpg


    I don't understand the second line. How does he separate the matrix in two different parts?
    Thanks for your time.
     
  2. jcsd
  3. Feb 13, 2014 #2
    Hi

    In the matrix product in the second line, the vector (cos(sigma + phi), sin(sigma+phi)) should be (cos(sigma), sin(sigma)), which when multiplied by R is by definition (x,y).

    Hope this helps.
     
  4. Feb 15, 2014 #3
    I don't know why he uses cos(σ+ψ) and sin(σ+ψ) instead of cos(σ) and sin(σ) when the matrix of the second line is separated.

    That would make cos(σ+ψ)=cos(σ). Is this true? I can't see that relation. Because there is no similarity between the triangles formed by the vector (x,y) and the vector (x',y'). So it's imposible the cosine is the same.
     
  5. Feb 16, 2014 #4
    I think it's just a mistake to be honest. It's definitely not true that cos(sigma + phi)=cos(sigma) for all values of these variables, so I think it's safe to assume it's just a mistake.
     
  6. Feb 17, 2014 #5
    Yes, it seems to be a mistake. But this mistake has helped me to analize better these concepts.
    Anyway, thank you!
     
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