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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.

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  1. experimentX
    • 3 years ago
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    |dw:1347894497129:dw|

  2. estudier
    • 3 years ago
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    geowotsit?

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

  4. experimentX
    • 3 years ago
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    |dw:1347894819011:dw|

  5. experimentX
    • 3 years ago
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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.

  6. experimentX
    • 3 years ago
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    it's a pretty famous problem ...

  7. estudier
    • 3 years ago
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    http://en.wikipedia.org/wiki/Brachistochrone_curve

  8. experimentX
    • 3 years ago
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    yep ... this is brachistochrome problem.

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

  10. estudier
    • 3 years ago
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    I was thinking geodesic at first, shortest distance....

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

  12. sauravshakya
    • 3 years ago
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    What about when h=w and h and approaches infinity

  13. sauravshakya
    • 3 years ago
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    h and w*

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

  15. experimentX
    • 3 years ago
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    * if w = 0 ...

  16. estudier
    • 3 years ago
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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)

  17. experimentX
    • 3 years ago
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    |dw:1347895370580:dw|

  18. sauravshakya
    • 3 years ago
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    I got that cycloid part........

  19. sauravshakya
    • 3 years ago
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    What if h and w approaches infinity.....

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

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

  22. experimentX
    • 3 years ago
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    yep ... this is a physics problem actually.

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

  24. sauravshakya
    • 3 years ago
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    Will it still be that cycloid

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

  26. sauravshakya
    • 3 years ago
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    OMG! This math stuff is out my level

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

  28. estudier
    • 3 years ago
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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)

  29. estudier
    • 3 years ago
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    or sphere, perhaps..

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

  31. sauravshakya
    • 3 years ago
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    It will only increase the length

  32. experimentX
    • 3 years ago
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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.

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

  34. sauravshakya
    • 3 years ago
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    oh

  35. experimentX
    • 3 years ago
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    trust me ... things aren't that intuitive.

  36. sauravshakya
    • 3 years ago
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    Ok..... I trust u. @experimentX

  37. sauravshakya
    • 3 years ago
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    When did u learnt these stuff. @experimentX

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

  39. sauravshakya
    • 3 years ago
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    At university

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

  41. experimentX
    • 3 years ago
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    told you i'm old guy

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