Search results for "brachistochrone"

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Overland flow generation on hillslopes of complex topography: analytical Solutions

2007

The analytical solution of the overland flow equations developed by Agnese et al. (2001; Hydrological Processes15: 3225–3238) for rectangular straight hillslopes was extended to convergent and divergent surfaces and to concave and convex profiles. Towards this aim, the conical convergent and divergent surfaces are approximated by a trapezoidal shape, and the overland flow is assumed to be always one-dimensional. A simple ‘shape factor’ accounting for both planform geometry and profile shape was introduced: for each planform geometry, a brachistochrone profile was obtained by minimizing a functional containing a slope function of the profile. Minima shape factors are associated with brachist…

brachistochroneRegular polygonGeometryConical surfaceFunction (mathematics)analytical solutionMaxima and minimaoverland flowSettore AGR/08 - Idraulica Agraria E Sistemazioni Idraulico-Forestaliconvergent and divergent hillslopeShape factorDivergence (statistics)Surface runoffoverland flow; convergent and divergent hillslopes; concave and convex profiles; analytical solution; brachistochroneconcave and convex profileBrachistochrone curveGeologyWater Science and Technology
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Historical Part—Calculus of Variations

2018

The calculus of variations is an old mathematical discipline and historically finds its origins in the introduction of the brachistochrone problem at the end of the 17th century by Johann Bernoulli to challenge his contemporaries to solve it. Here, we briefly introduce the reader to the main results.

Bernoulli's principleCalculusCalculus of variationsBrachistochrone curveMathematics
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