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Find a shape of inclined plane(not necessarily plane) that takes shortest time to reach from top to bottom. Assume the ball is sliding without any friction.
 one year ago
 one year ago
Find a shape of inclined plane(not necessarily plane) that takes shortest time to reach from top to bottom. Assume the ball is sliding without any friction.
 one year ago
 one year ago

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experimentXBest ResponseYou've already chosen the best response.1
dw:1347894497129:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
assume both h and w are not zero.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1347894819011:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
could you all delete your answers. I missed to put that the ball is sliding gliding with no friction. yep cycloid.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
it's a pretty famous problem ...
 one year ago

estudierBest ResponseYou've already chosen the best response.1
http://en.wikipedia.org/wiki/Brachistochrone_curve
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yep ... this is brachistochrome problem.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
cycloid is a shape made my rolling circle. http://en.wikipedia.org/wiki/Cycloid
 one year ago

estudierBest ResponseYou've already chosen the best response.1
I was thinking geodesic at first, shortest distance....
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
i did this with calculus of variation. haven't done this with purely calculus.
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
What about when h=w and h and approaches infinity
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
take a circle with zero radius, you will get a straight line.
 one year ago

estudierBest ResponseYou've already chosen the best response.1
http://www.cmsim.eu/papers_pdf/january_2012_papers/25_CMSIM_2012_Pokorny_1_281298.pdf (brachistochrone as special case of geodesic)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1347895370580:dw
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
I got that cycloid part........
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
What if h and w approaches infinity.....
 one year ago

estudierBest ResponseYou've already chosen the best response.1
It will never get to the bottom and you will never know..:)
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Then I think this should work:dw:1347895555863:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yep ... this is a physics problem actually.
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Oh ya @estudier ........ But what if h and w are very large.... but some finite number
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Will it still be that cycloid
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yep .. it should be cycloid ... make by a huge circle.
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
OMG! This math stuff is out my level
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Didnt get why cycloid........ I just know we need to maximise the accleration
 one year ago

estudierBest ResponseYou've already chosen the best response.1
Maybe at infinity, you have to go to some other mathematical model, maybe conformal, to analyze that (in conformal everything is a circle, point is circle with zero radius, line is infinite circle etc)
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
I mean why cycloid is the answer to @experimentX question
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
It will only increase the length
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
well ... this is easily solved with calculus of variation. probably you need to be half way through undergrad to encounter calculus of variation.
 one year ago

estudierBest ResponseYou've already chosen the best response.1
When you solve the problem, that's what comes out, a deeper meaning, you mean?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
trust me ... things aren't that intuitive.
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Ok..... I trust u. @experimentX
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
When did u learnt these stuff. @experimentX
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
i was wondering if anyone could solve it using purely calculus. I haven't tried it yet.
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
I will think on this problem.... see If I can get to the solution
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
told you i'm old guy
 one year ago
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