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 2 years 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.
 2 years 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.

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experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1347894497129:dw

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1assume both h and w are not zero.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1347894819011:dw

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1it's a pretty famous problem ...

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1yep ... this is brachistochrome problem.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1cycloid is a shape made my rolling circle. http://en.wikipedia.org/wiki/Cycloid

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1I was thinking geodesic at first, shortest distance....

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1i did this with calculus of variation. haven't done this with purely calculus.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1What about when h=w and h and approaches infinity

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1take a circle with zero radius, you will get a straight line.

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1347895370580:dw

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1I got that cycloid part........

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1What if h and w approaches infinity.....

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1It will never get to the bottom and you will never know..:)

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1Then I think this should work:dw:1347895555863:dw

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1yep ... this is a physics problem actually.

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1Will it still be that cycloid

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1yep .. it should be cycloid ... make by a huge circle.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1OMG! This math stuff is out my level

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1Didnt get why cycloid........ I just know we need to maximise the accleration

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1Maybe 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)

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1I mean why cycloid is the answer to @experimentX question

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1It will only increase the length

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

estudier
 2 years ago
Best ResponseYou've already chosen the best response.1When you solve the problem, that's what comes out, a deeper meaning, you mean?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1trust me ... things aren't that intuitive.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1Ok..... I trust u. @experimentX

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1When did u learnt these stuff. @experimentX

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1i was wondering if anyone could solve it using purely calculus. I haven't tried it yet.

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.1I will think on this problem.... see If I can get to the solution

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1told you i'm old guy
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