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Meaning Of Cylindrical VECTOR

  1. Jan 24, 2009 #1
    1. IM very confused about the meaning of these cylindrical vectors

    for Cartesian vectors if i say A = 1ax + 2ay + 3az

    I know i mean a vector with a magntiude of 1 in the x direction 2 in the y direction and 3 in the z direction and i make a line from the origin to point (1,2,3).

    Now for cylindrical I cannot think the same way

    for a point i can make a point easily it seems to have a similar meaning (r is the magntiude from origin to the point, phi being the angle from x and z being the regular z)


    now for a vector example a = 1 ap + 2 aphi + 3 az


    Im very confused how do i draw this vector and what does it mean???



    the magntiude along p is 1 so the angle is 2? from the x axis?????

    i dont think this is correct.. I cant understand this help!!!


     
  2. jcsd
  3. Jan 24, 2009 #2
    Cylindrical coordinates can be thought of as a right triangle with a point of rotation at the origin. The one leg of the triangle lies in the x-y plane and is

    [tex]\rho[/tex]

    and the vertical leg is

    [tex]\mbox{z}[/tex]

    and the angle with respect to an axis, usually the x axis, that the triangle is rotated from is

    [tex]\phi[/tex]

    These three values form another orthogonal coordinate system but it is not fixed like a Cartesian coordinate system but changes direction as the point changes position.
     
    Last edited: Jan 24, 2009
  4. Jan 24, 2009 #3
    so you would not be able to draw the vector out?

    how would i draw or specifiy a change in aphi


    like on a 3d plane what would the difference of

    1 ap + 2aphi + 3az and 1 ap + 3aphi + 3az ?
     
  5. Jan 24, 2009 #4
  6. Jan 24, 2009 #5
    the thing is this all seems to be about points i dont understand how to relate it to vectors in cylindrical system

    I was wondering if someone can give me an idea of how to represent a vector in cylindrical coordinate system.

    like on a 3d plane what would the difference of

    1 ap + 2aphi + 3az and 1 ap + 3aphi + 3az ?
     
  7. Jan 24, 2009 #6
    I think what you are looking for is a relation between the Cartesian vectors and the Cylindrical vectors. So, using the picture from the link given previously and some trigonometry, we have

    [tex]\vec{x}=\rho\mbox{cos\phi}\hat{x}[/tex]

    [tex]\vec{y}=\rho\mbox{sin\phi}\hat{y}[/tex]

    [tex]\vec{z}=z\hat{z}[/tex]

    where

    [tex]\hat{x},\hat{y}, and \ \hat{z}[/tex]

    are unit vectors in the x, y, and z directions. The inverse relations are

    [tex]\vec{\rho}=\sqrt{x^2+y^2}\hat{\rho}[/tex]

    [tex]\vec{\phi}=\arctan{\frac{y}{x}}\hat{\phi}[/tex]

    The z value is the same for both coordinate systems. Hope this helps.
     
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