Stokes equation help

  • Thread starter supercali
  • Start date
  • #1
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Homework Statement


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]

Homework 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
 
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Answers and Replies

  • #2
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Would x = 1 + 2 cos(t), y = 2 + 2 sin(t) and z = -1/2 - 2 sin(t) do the trick?
 
  • #3
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i wonder if it is allowed given we have to do a multiple integral needing 2 variables
 
  • #4
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Why wouldn't you just use Green's?
 
  • #5
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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)
 
  • #6
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See what Halls answered you in the other thread.
 

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