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Stokes equation help

  1. Aug 21, 2008 #1
    1. The problem statement, all variables and given/known data
    let F be vector field:
    [tex]\[\vec F = \cos (xyz)\hat j + (\cos (xyz) - 2x)\hat k\] [/tex]
    let L be the the curve that intersects between the cylinder [tex]\[(x - 1)^2 + (y - 2)^2 = 4
    \][/tex] and the plane y+z=3/2
    calculate:
    [tex]\[\left| {\int {\vec Fd\vec r} } \right|\][/tex]

    2. Relevant equations
    in order to solve this i thought of using the stokes theorem because the normal to the plane is [tex] \[\frac{1}{{\sqrt 2 }}(0,1,1)\] [/tex]
    thus giving me
    [tex]\oint{Fdr}=\int\int{curl(F)*n*ds}=\int\int{2/sqrt{2}*\sin(xyz)}[/tex]


    i tried to parametries x y and z x= rcos(t)+1 y=rsin(t)+2 z=1/2-rsin(t)

    but it wont work
     
    Last edited by a moderator: Aug 21, 2008
  2. jcsd
  3. Aug 21, 2008 #2
    Re: stokes

    Would x = 1 + 2 cos(t), y = 2 + 2 sin(t) and z = -1/2 - 2 sin(t) do the trick?
     
  4. Aug 21, 2008 #3
    Re: stokes

    i wonder if it is allowed given we have to do a multiple integral needing 2 variables
     
  5. Aug 21, 2008 #4
    Re: stokes

    Why wouldn't you just use Green's?
     
  6. Aug 21, 2008 #5
    Re: stokes

    using green or stokes is the same thing green is just a private solution of stokes and if you use it you are still stuck with that sin(xyz)
     
  7. Aug 21, 2008 #6
    Re: stokes

    See what Halls answered you in the other thread.
     
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