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Transform Cylindrical coordinates into Cartesian Coordiantes

  1. Oct 8, 2014 #1
    I've learned that a vector in coordinate system can be expressed as follows:
    A = axAx+ayAy+azAz.
    ai, i = x, y, z, are the base vectors.
    The transformation matrix from cylindrical coordinates to cartesian coordiantes is:
    Ax cosΦ -sinΦ 0 Ar
    Ay = sinΦ cosΦ 0 mutiplye by AΦ
    Az 0 0 1 Az

    and the conversion formula
    x = rcosΦ
    y = rsinΦ
    z = z

    1. What's the difference between this two kind of equations?
    2. Why Ax is not equal to x?
    3. I was told that Ax might be a function of x, y and z. Is the latter kind of equaltions has a prerequisite that ax = (1, 0, 0), but in the first kind of equations, the base vector can be anything else?
    4. From the matrix, Ax = cosΦAr - sinΦAΦ, that is not equal to x = rcosΦ !? Why? How should I apply the transformation matrix?
    Thanks in advance.
     
  2. jcsd
  3. Oct 8, 2014 #2

    mathman

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    Ax cosΦ -sinΦ 0 Ar
    Ay = sinΦ cosΦ 0 mutiplye by AΦ
    Az 0 0 1 Az
    Above is confusing - looks like typos.
     
  4. Oct 8, 2014 #3
    sorry, it should be Unnamed QQ Screenshot20141009091728.png . The formula was not inserted successfully.
     
    Last edited: Oct 8, 2014
  5. Oct 9, 2014 #4

    mathman

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    The matrix formulation looks like a rotation of the (x,y) coordinates around the z axis through an angle φ, not a conversion from cylindrical to cartesian coordinates.
     
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