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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What is the position as a function of time for a mass falling down a cycloid curve?
In the brachistochrone problem and in the tautochrone problem it is easy to see that a cycloid is the curve that satisfies both problems.
If we consider $x$ the horizontal axis and $y$ the vertical ...
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Brachistochrone Problem for Inhomogeneous Potential
This recent question about holes dug through the Earth led me to wonder: if I wanted to dig out a tube from the north pole to the equator and build a water slide in it, which shape would be the ...
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Another Solution To Brachistochrone Problem
Recalling the statement of the problem :
Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the ...
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Path to obtain the shortest traveling time
Asume we have a particle sitting at the point A(0,0) in a gravitational field.
(g=9.81) It is going to move along some path to the point B(a,b) Where a>0 and b<0.
What is the curve the particle ...
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Is there an intuitive reason the brachistochrone and the tautochrone are the same curve?
The brachistochrone problem asks what shape a hill should be so a ball slides down in the least time. The tautochrone problem asks what shape yields an oscillation frequency that is independent of ...
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What is the intuitive reason that the trajectory of a charged particle in a uniform crossed electro-magnetic field is a brachistochrone?
Cycloid is a type of trajectory which is traced by a point on the circumference of a planar circle rolling without slipping on a surface. It turns out that this is the solution to the Brachistochrone ...
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Brachistochrone problem for 3 points
I wonder how I can solve the Brachistochrone problem for 3 points?
The matter starts from point A that is the highest point and it must pass from B and must finish with point C. (No any friction in ...
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What shape of track minimizes the time a ball takes between start and stop points of equal height?
I was at my son's high school "open house" and the physics teacher did a demo with two curtain rail tracks and two ball bearings. One track was straight and on a slight slope. The beginning and end ...
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Brachistochrone problem in general relativity
This question Brachistochrone Problem for Inhomogeneous Potential has the obvious extension. Namely the same question, when gravity is treated according to general relativity. To make it specific let'...
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Could two concatenated cycloids be an optimal solution to the Brachistochrone problem?
The following is a specific instance of the brachistochrone
problem, which I first encountered in grad school, and I
have occasionally used as hw problem in teaching CM.
A particle is started from ...
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Ball on a slope with hollow
The experiment shown in the image suggests that ball B will reach the goal faster than ball A although the balls have identical properties and they start from the same height.
The authors even ...
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Brachistochrone to a vertical line [closed]
Just for fun, I am working through some problems in Mathematics of Classical and Quantum Physics by Byron and Fuller. Problem 2.13 reads:
Prove that a particle moving under gravity in a plane from a ...
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Curved Slope faster than linear?
So I saw this gif the other day, and was wondering, is this real or fake? And supposing there is no energy dissipated by the friction, why does such thing occur?
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