What is the brachistochrone problem and how does it affect society?

[zeithief]

Hi all, I'm a maths and physics student from college. I have been asked by tutor to make a small report on the uses of calculus of variation which has an impact of society... I have been searching up and down but can't find anything specific or easy enough to understand on the internet.. I was wondering if anyone here has some website for me to refer to or any ideas on what i can do. Thanks in advance :D

 

[arildno]

Since a heck of a lot of the fundamental equations in physics can be regarded as derivable from a principle of variation, the calculus of variation can be regarded as having the same applicability as physics has..

For further note, do not post your questions in the tutorials section.

 

[zeithief]

can you like point out an specific case in which the application of calculus of variation which has an impact of society? and sorry, i didnt saw the homework section!

 

[arildno]

Can you point to a specific case where physics has impact on our society?
One classic example is elasticity theory, another is the concept of geodesics, as they appear in general relativity.
A third example is Fermat's principle for the propagation of light.

 

[zeithief]

ok! thanks!

 

[Jheriko]

You should search the web for "the action principle" and the "Euler-Lagrange equation" which make use of functional derivatives. "Feynman path integrals" are a more well known example and give a nice example of the functional integral.

These methods are very important in quantum mechanics, which has had a huge effect on society, e.g. technology, philosophy, entertainment, etc..

 

[Agnostic]

Do a search on the "the brachystochrone problem" or Hamilton’s Principle...

 

[Hurkyl]

You mean "The brachistrone problem"

 

[Agnostic]

You mean "The brachistrone problem"

No. I mean exactly what I said :)


brachysto / chrone

Greek for: Shortest / Time

The actual originial correct spelling is brachistochrone.