## experimentX 3 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.

1. experimentX

|dw:1347894497129:dw|

2. estudier

geowotsit?

3. experimentX

assume both h and w are not zero.

4. experimentX

|dw:1347894819011:dw|

5. experimentX

could you all delete your answers. I missed to put that the ball is sliding gliding with no friction. yep cycloid.

6. experimentX

it's a pretty famous problem ...

7. estudier
8. experimentX

yep ... this is brachistochrome problem.

9. experimentX

cycloid is a shape made my rolling circle. http://en.wikipedia.org/wiki/Cycloid

10. estudier

I was thinking geodesic at first, shortest distance....

11. experimentX

i did this with calculus of variation. haven't done this with purely calculus.

12. sauravshakya

What about when h=w and h and approaches infinity

13. sauravshakya

h and w*

14. experimentX

take a circle with zero radius, you will get a straight line.

15. experimentX

* if w = 0 ...

16. estudier

http://www.cmsim.eu/papers_pdf/january_2012_papers/25_CMSIM_2012_Pokorny_1_281-298.pdf (brachistochrone as special case of geodesic)

17. experimentX

|dw:1347895370580:dw|

18. sauravshakya

I got that cycloid part........

19. sauravshakya

What if h and w approaches infinity.....

20. estudier

It will never get to the bottom and you will never know..:-)

21. sauravshakya

Then I think this should work:|dw:1347895555863:dw|

22. experimentX

yep ... this is a physics problem actually.

23. sauravshakya

Oh ya @estudier ........ But what if h and w are very large.... but some finite number

24. sauravshakya

Will it still be that cycloid

25. experimentX

yep .. it should be cycloid ... make by a huge circle.

26. sauravshakya

OMG! This math stuff is out my level

27. sauravshakya

Didnt get why cycloid........ I just know we need to maximise the accleration

28. estudier

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)

29. estudier

or sphere, perhaps..

30. sauravshakya

I mean why cycloid is the answer to @experimentX question

31. sauravshakya

It will only increase the length

32. experimentX

well ... this is easily solved with calculus of variation. probably you need to be half way through undergrad to encounter calculus of variation.

33. estudier

When you solve the problem, that's what comes out, a deeper meaning, you mean?

34. sauravshakya

oh

35. experimentX

trust me ... things aren't that intuitive.

36. sauravshakya

Ok..... I trust u. @experimentX

37. sauravshakya

When did u learnt these stuff. @experimentX

38. experimentX

i was wondering if anyone could solve it using purely calculus. I haven't tried it yet.

39. sauravshakya

At university

40. sauravshakya

I will think on this problem.... see If I can get to the solution

41. experimentX

told you i'm old guy