Brachistochrone curve - Wikipedia, the free encyclopedia
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A Brachistochrone curve (Gr. βραχίστος, brachistos - the shortest , χρόνος, chronos - time ), or curve of fastest descent, is the curve between two points that is covered in the least time by a ...
en.wikipedia.org/wiki/Brachistochrone_curve
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The brachistochrone problem was posed by Johann Bernoulli in Acta Eruditorum in June 1696. He introduced the problem as follows:- ... Johann Bernoulli was not the first to consider the brachistochrone problem. Galileo in 1638 had studied the problem in his famous work Discourse on two new sciences. His version of the...
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www-history.mcs.st-and.ac.uk/HistTopics/Brachistochrone...
www-history.mcs.st-and.ac.uk/HistTopics/Brachistochrone.html
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The brachistochrone problem, that is, "find the path of shortest time of a particle moving between two points on a vertical plane", was proposed, solved erroneously, and studied experimentally by Galileo, and solved mathematically by Jacques Bernoulli's variational calculus methods in 1697. We will revisit...
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www.sewanee.edu/Physics/TAAPT/TAAPTTALK.html
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The National Curve Bank Project for Students of Mathematics ... Johnson, Nils P., The Brachistochrone Problem, The College Mathematics Journal, vol. 35 (3), May 2004, pp. 192-197. ... ; The Brachistochrone; The Famous Problem of Fastest Descent: A Classic among All Classics;
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curvebank.calstatela.edu/brach/brach.htm
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The brachistochrone problem asks for the shape of the curve down which a bead, starting from rest and accelerated by gravity, will slide (without friction) from one point to another in the least time.
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demonstrations.wolfram.com/BrachistochroneProblem/
demonstrations.wolfram.com/BrachistochroneProblem/
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Brachistochrone Problem/Calculus of Variations Advanced Physics discussion ... Brachistochrone Problem/Calculus of Variations Share It Thread Tools Search this Thread...
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www.physicsforums.com/showthread.php?t=135842
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Johann Bernoulli was not the first to consider the brachistochrone problem. Galileo in 1638 had studied the problem in his famous work Discourse on two new sciences. His version of the problem was first to find the straight line from a point A to the point on a vertical line which it would reach the quickest.
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www-history.mcs.st-andrews.ac.uk/history/PrintHT/Brachi...
www-history.mcs.st-andrews.ac.uk/history/PrintHT/Brachistochrone.html
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The brachistochrone problem thus becomes the following: A particle moves from A to B in such a way that whenever its vertical drop from A is y, its speed is given by (3). Find the AB-curve with the shortest traversal time.
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www.math.umt.edu/tmme/vol5no2and3/TMME_vol5nos2and3_a1_...
www.math.umt.edu/tmme/vol5no2and3/TMME_vol5nos2and3_a1_pp.169_184.pdf
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The brachistochrone problem is a seventeenth century exercise in the calculus of variations. In his solution to the problem, Jean Bernoulli employed a very clever analogy to prove that the path is a cycloid.
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whistleralley.com/brachistochrone/brachistochrone.htm
whistleralley.com/brachistochrone/brachistochrone.htm
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