Applications of the Kelvin-Stokes Theorem

In summary, the conversation is about potential applications of the Kelvin-Stokes Theorem, a mathematical theorem that relates line integrals of vector fields to surface integrals. The conversation mentions the basic application of calculating work done on a particle moving through a vector field, but also seeks suggestions for more creative and complex problems, such as calculating the work done by gravity on a tilted Ferris wheel. It is mentioned that Stokes' theorem is commonly used in classical electromagnetism, specifically in two of Maxwell's equations. The conversation concludes by stating that the discussion is not related to homework, but rather for enjoyment and exploration.
  • #1
Physics-Pure
29
0
Hi Guys~

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 ℝ3. 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.
 
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  • #2
Stokes' theorem is used in classical electromagnetism. After all, two of Maxwell's equations involve the curl.
 

FAQ: Applications of the Kelvin-Stokes Theorem

What is the Kelvin-Stokes Theorem?

The Kelvin-Stokes Theorem is a mathematical theorem that relates the line integral of a vector field over a closed curve to the surface integral of the curl of the vector field over the surface enclosed by that curve. In simpler terms, it describes the relationship between a line integral and a surface integral.

What are some real-world applications of the Kelvin-Stokes Theorem?

The Kelvin-Stokes Theorem has many applications in various fields such as physics, engineering, and fluid dynamics. It is commonly used to analyze fluid flow, calculate work done by a force, and study electromagnetism.

How is the Kelvin-Stokes Theorem related to Stokes' Theorem?

The Kelvin-Stokes Theorem and Stokes' Theorem are closely related. The Kelvin-Stokes Theorem is a special case of Stokes' Theorem, which is a more general theorem that relates a line integral to a surface integral.

What are the assumptions and limitations of the Kelvin-Stokes Theorem?

The Kelvin-Stokes Theorem assumes that the vector field and the surface over which the integrals are calculated are continuous and differentiable. It also only applies to closed curves and surfaces, meaning that the starting and ending points of the curve must be the same.

How is the Kelvin-Stokes Theorem used in computer simulations and modeling?

The Kelvin-Stokes Theorem is commonly used in computer simulations and modeling to analyze and predict fluid flow and other physical phenomena. By using this theorem, researchers and engineers can calculate the behavior of complex systems and make more accurate predictions.

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