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Research Papers

The Brachistochrone With a Movable End-Point and the Nonsimultaneous Variations

[+] Author and Article Information
D. Radomirovic

 Faculty of Agriculture, Novi Sad, Serbia

Dj. Djukic, L. Cveticanin

 Faculty of Technical Sciences, Novi Sad, Serbia

J. Comput. Nonlinear Dynam 5(1), 011007 (Nov 18, 2009) (7 pages) doi:10.1115/1.4000316 History: Received October 07, 2008; Revised May 13, 2009; Published November 18, 2009; Online November 18, 2009

In this paper, the necessary and sufficient conditions for minima plane path with a movable end-point are developed. Using the calculus of variations the considered conditions are based on the zero first-order nonsimultaneous variation and on the positive second-order variation in the functional of integral type corresponding to mechanical systems. The applied procedure is the coordinate parametric method. The obtained solutions are tested on a brachistochrone with one end-point constrained to lie on a circle. The exact solution is compared with the approximate one obtained with Ritz’s method.

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