Electronic Proceedings of the Eighteenth Annual International Conference on Technology in Collegiate Mathematics

Orlando, Florida, March 16-19, 2006

Paper C037

This is an electronic reprint, reproduced by permission of Pearson Education Inc. Originally appeared in the Proceedings of the Eighteenth Annual International Conference on Technology in Collegiate Mathematics, Edited by Joanne Foster, ISBN 0-321-49160-2, Copyright (C) 2007 by Pearson Education, Inc.


Finding the Brachistochrone Between Two Points in a Vertical Plane by Direct Numerical Integration

Jay Villanueva


Florida Memorial University
Miami, FL 33054
USA


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ABSTRACT

In 1696, Bernoulli proposed determining the 'curve of quickest descent' between two points in a vertical plane. As is well known, the solution involves finding a function to make an integral an extreme. Here we verify this by numerically calculating the transit time between two points joined by various curves.

Keyword(s): numerical methods, calculus