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I Calculus of variations

  1. Aug 19, 2017 #1
    when inducing that the cycloid is the least time-taking course between the two points in the two dimension, we have to use calculus of variations.

    Then is it possible to induce the parameter of the least time-taking course between two points in the three dimension?
  2. jcsd
  3. Aug 20, 2017 #2


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    In principle yes, in fact the cycloid solution applies to a 3D curve when the two points lie in a plane that also contains the gravitational force vector. Since such plane always exists for any given pair of points, the trajectory will always be a cycloid.
    Last edited: Aug 20, 2017
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