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Differential Length (Cylindrical Coordinates)

  1. Jan 24, 2009 #1
    So we just were given some formulas and I am confused about this simple question

    Find the differential length or distance between the two points.

    P(2,pi/2,-1) and Q(5,3pi/2,5)


    I know this

    for cylindrical

    dL = dp (ap) + p dphi (aphi) + dz (az)

    So i would integrate

    I have a few questions does it matter if for example for dp

    i integrate from 2 to 5 or from 5 to 2?

    also in the aphi part, there is a "p" which is not constant in my problem so how can i do the integral with respect to dphi when p is not constant!!!

    can I even use this?

    help


    EDITED: MY TEXT USES A DIFFERENT NOTATION I POSTED ANOTHER QUESTION AND THE INDIVIDUAL ALSO HAD PROBLEMS WITH MY NOTATION I HOPE THIS DIAGRAM HELPS IT'S FROM MY TEXTBOOK:

    [​IMG]
     
    Last edited: Jan 25, 2009
  2. jcsd
  3. Jan 25, 2009 #2

    Gib Z

    User Avatar
    Homework Helper

    I am a bit confused as to your notation but;

    It does matter which order you integrate from. By convention length must be a positive quantity and so our integral must output positive values. Choosing the integral with upper limit of integration as 5, and lower limit as 2, we achieve that, but if we were to do it the other way around, the value we would get is negative.

    Also, I'm a bit confused as to what specifically you are talking about, but if the integral is with respect to the variable phi, and that variable is not a function of p, even if p is not a constant within the whole problem we can regard it as a constant within the integral.
     
  4. Jan 25, 2009 #3
    But if I were to have any integral say

    Integral of (ydx)

    I have understand from my courses I cannot do this integral since y is not a function of x. But you are saying just treat it like a constant?
     
  5. Jan 25, 2009 #4
    Pi and phi are constants yes.
     
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