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I was wondering if anyone had any suggestions for applications of the Kelvin-Stokes Theorem. Recall that the Kelvin-Stokes Theorem states: http://upload.wikimedia.org/math/0/4/4/04402b2d910114267bffa0e030445af6.png

(Check Wikipedia for further explanation)

Obviously one could apply this in it's most basic form to calculate the work done upon a particle moving through a vector field in ℝ

^{3}. But I'm looking for some "weirder" problems.

i.e.

Imagine a tilted Ferris wheel rotating on the Earth. You want to calculate the work done by gravity on the Ferris wheel. The Ferris wheel is a closed path so Stokes' theorem holds.

Something of that nature. Anyone have any suggestions on how to go about a problem like this ^?

or any other problem that you may know of relating to this.

Thank you,

Physics-Pure

P.S. This is not homework related, purely for fun.