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Co-ordinates transformation

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi i have a question that how to convert the co-ordinates according to following statement?
    Its no difficult to solve the simple conversion but the bold one are confusing me.


    A=4x-2y-4z
    Transform it into cylindrical co-ordinate system at P (ρ=4, ϕ=120o ,z=2)

    B=15x+10y
    Transform it into cylindrical co-ordinate system at P(x=3, y=4, z=-1)





    2. The attempt at a solution

    Equations for converting Cartesian to cylindrical coordinates:

    r= [x2 + y21/2
    ϕ= tan-1= y/x
    z=z

    by putting values
    For First question:
    r=√20=4.472
    ϕ= -26.57
    z=-4

    For Second question:
    r= 18.03
    ϕ= 33.69
    z=0
     
  2. jcsd
  3. Jan 26, 2012 #2

    vela

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    This is common point of confusion. What you've done is convert the Cartesian coordinates (4, -2, -4) to the equivalent cylindrical coordinates. What the problem is asking you to do, however, is different.

    Take a look at the diagram at the start of this page:

    http://mathworld.wolfram.com/CylindricalCoordinates.html

    At each point, there are associated unit vectors ##\hat{\rho}##, ##\hat{\phi}##, and ##\hat{z}##. Their directions depend on which point you're at. For example, if you're at the point (1, 0, 0), ##\hat{\rho}## would point along the +x-direction, and ##\hat{\phi}## would point in the +y direction. If you're at the point (0, 1, 0), ##\hat{\rho}## would point in the +y direction, and ##\hat{\phi}## would point in the -x direction.

    Given the information in bold, you can figure out what ##\hat{\rho}## and ##\hat{\phi}## are. ##\hat{z}## always points in the +z direction. Once you know what the unit vectors are equal to, you're supposed to express the vectors A and B in terms of them.
     
  4. Jan 26, 2012 #3
    unfortunately i can't understand from that given link, kindly give an example by solving one of the equation or any of. . .
     
  5. Jan 26, 2012 #4

    vela

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    Sorry, we don't do your homework for you here. If you can't see what I tried to explain from the diagram, I suggest you consult your textbook for a more detailed explanation.
     
  6. Jan 27, 2012 #5
    I doesn't mean that, i just want to say that, if you please tell this by example by taking any random point P, if such an example is given on text book, i don't need to refer from internet
     
  7. Jan 27, 2012 #6

    vela

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    My point was that I would have liked to see even a minimal attempt from you to try understand what's going on instead of simply saying "I don't get it."

    Say you have a vector field ##\vec{V}(\vec{r})##, and at both ##\vec{r}=(1, 0, 0)## and ##\vec{r}=(0, 1, 0)##, it points in the +x direction.

    At the point (1, 0, 0), you'd say ##\vec{V}(1, 0, 0) = \hat{\rho}##. At the point (0, 1, 0), however, the basis vectors point in different directions. In this case, you'd have ##\vec{V}(0, 1, 0) = -\hat{\phi}##.
     
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