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experimentX Group Title

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
  • 2 years ago

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  1. experimentX Group Title
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    |dw:1347894497129:dw|

    • 2 years ago
  2. estudier Group Title
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    geowotsit?

    • 2 years ago
  3. experimentX Group Title
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    assume both h and w are not zero.

    • 2 years ago
  4. experimentX Group Title
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    |dw:1347894819011:dw|

    • 2 years ago
  5. experimentX Group Title
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    could you all delete your answers. I missed to put that the ball is sliding gliding with no friction. yep cycloid.

    • 2 years ago
  6. experimentX Group Title
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    it's a pretty famous problem ...

    • 2 years ago
  7. estudier Group Title
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    http://en.wikipedia.org/wiki/Brachistochrone_curve

    • 2 years ago
  8. experimentX Group Title
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    yep ... this is brachistochrome problem.

    • 2 years ago
  9. experimentX Group Title
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    cycloid is a shape made my rolling circle. http://en.wikipedia.org/wiki/Cycloid

    • 2 years ago
  10. estudier Group Title
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    I was thinking geodesic at first, shortest distance....

    • 2 years ago
  11. experimentX Group Title
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    i did this with calculus of variation. haven't done this with purely calculus.

    • 2 years ago
  12. sauravshakya Group Title
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    What about when h=w and h and approaches infinity

    • 2 years ago
  13. sauravshakya Group Title
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    h and w*

    • 2 years ago
  14. experimentX Group Title
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    take a circle with zero radius, you will get a straight line.

    • 2 years ago
  15. experimentX Group Title
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    * if w = 0 ...

    • 2 years ago
  16. estudier Group Title
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    http://www.cmsim.eu/papers_pdf/january_2012_papers/25_CMSIM_2012_Pokorny_1_281-298.pdf (brachistochrone as special case of geodesic)

    • 2 years ago
  17. experimentX Group Title
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    |dw:1347895370580:dw|

    • 2 years ago
  18. sauravshakya Group Title
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    I got that cycloid part........

    • 2 years ago
  19. sauravshakya Group Title
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    What if h and w approaches infinity.....

    • 2 years ago
  20. estudier Group Title
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    It will never get to the bottom and you will never know..:-)

    • 2 years ago
  21. sauravshakya Group Title
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    Then I think this should work:|dw:1347895555863:dw|

    • 2 years ago
  22. experimentX Group Title
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    yep ... this is a physics problem actually.

    • 2 years ago
  23. sauravshakya Group Title
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    Oh ya @estudier ........ But what if h and w are very large.... but some finite number

    • 2 years ago
  24. sauravshakya Group Title
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    Will it still be that cycloid

    • 2 years ago
  25. experimentX Group Title
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    yep .. it should be cycloid ... make by a huge circle.

    • 2 years ago
  26. sauravshakya Group Title
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    OMG! This math stuff is out my level

    • 2 years ago
  27. sauravshakya Group Title
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    Didnt get why cycloid........ I just know we need to maximise the accleration

    • 2 years ago
  28. estudier Group Title
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    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)

    • 2 years ago
  29. estudier Group Title
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    or sphere, perhaps..

    • 2 years ago
  30. sauravshakya Group Title
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    I mean why cycloid is the answer to @experimentX question

    • 2 years ago
  31. sauravshakya Group Title
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    It will only increase the length

    • 2 years ago
  32. experimentX Group Title
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    well ... this is easily solved with calculus of variation. probably you need to be half way through undergrad to encounter calculus of variation.

    • 2 years ago
  33. estudier Group Title
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    When you solve the problem, that's what comes out, a deeper meaning, you mean?

    • 2 years ago
  34. sauravshakya Group Title
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    oh

    • 2 years ago
  35. experimentX Group Title
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    trust me ... things aren't that intuitive.

    • 2 years ago
  36. sauravshakya Group Title
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    Ok..... I trust u. @experimentX

    • 2 years ago
  37. sauravshakya Group Title
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    When did u learnt these stuff. @experimentX

    • 2 years ago
  38. experimentX Group Title
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    i was wondering if anyone could solve it using purely calculus. I haven't tried it yet.

    • 2 years ago
  39. sauravshakya Group Title
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    At university

    • 2 years ago
  40. sauravshakya Group Title
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    I will think on this problem.... see If I can get to the solution

    • 2 years ago
  41. experimentX Group Title
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    told you i'm old guy

    • 2 years ago
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