Questions tagged [brachistochrone-problem]
the problem of finding the path between two points such that the transit time under specified conditions is minimized.
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Brachistochrone problem with drag
The original Brachistochrone problem is without friction and drag. The Brachistochrone problem can also be solved analytically with friction. But what would the optimal path be if there was a drag ...
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Brachistochrone Problem for Spacecraft
I understand how the Brachistochrone Problem works, and do understand how the friction is added to it, however I am unsure of how to use the Brachistochrone Problem for use in spacecraft.
We know ...
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Variation of functional with respect to Lagrange multiplier in QM
So, I am reading a paper on Quantum Brachistochrome and on the second page they say that they are doing a variation w.r.p. $<\phi|$, (which is a lagrange mulriplier) of the following action:
$$ S(\...
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Fermat least time and snell's law for multiple layers of medium
I am reading a differential equation book that discusses the Brachistochrone problem. The book discusses Bernoulli's solution that uses Snell's law. The book says that a ray would follow the fastest ...
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Non-differentiable solution of the Brachistochrone problem
Is there a solution to the brachistochrone problem where the solution is non-differentiable everywhere (angular point)?
The Euler-Lagrange method fails if the first or second derivative of the ...
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Is this idea/concept very useful to alternatively tackle a brachistochrone problem?
As we know initially we would be given two points on a 2D surface (consider a plane perpendicular to ground ) we would like to run a small ball from higher level point to lower level point from a ...
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Hypocyloid Integral in Polar Coordinates
I've been working on the classic problem of finding the path through which a body travels in least time between two points on the surface of the Earth, assuming that the body is allowed to fall ...
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Explanation for extra portion of Brachistochrone curve?
https://en.wikipedia.org/wiki/Brachistochrone_curve
In this article, it points out that the curve taking the shortest time from point A to point B under constant acceleration has a different segment ...
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