A ball sliding along a 'Lemniscate' curve takes the same time to arrive at a given point as a ball that takes the direct pathpic.twitter.com/a8FtMonFiE
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How are these curves found
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Ty I'll read up on it!
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I think in this case it is found by solving an Abel-type integral equation. Otherwise, I do not see how the extremum requirement is formulated.
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I was trying to find that curve by myself. I found this differential equation : I assumed that the parametrisation is normalized (norm(gamma'(s)) = 1) in order to get a unique parametrization for any curve.pic.twitter.com/FFwSnIJ5OT
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Where gamma is the parametrization of the curve, gamma_1 its x coordinate and gamma_2 its why coordinates. However, i do not have the slightest idea on how to solve it, neither express it as a Cauchy problem that matlab could numerically solve for me.
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