Application of fundamental lemma of variational calculus to the problem for the brachistochrone

Risteska, Aleksandra and Kokalanov, Vasko and Gicev, Vlado (2015) Application of fundamental lemma of variational calculus to the problem for the brachistochrone. In: ITRO 2015, 26 June 2015, Zrenjanin, Serbia.

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Abstract

Variational calculus studied methods for finding maximum and minimum values of functional. It has its inception in 1696 year by Johan Bernoulli with its glorious problem for the brachistochrone: to find a curve, connecting two points A and B , which does not lie in a vertical, so that heavy point descending on this curve from position A to reach position in for at least time. In functional analysis variational calculus takes the same space, as well as theory of maxima and minimum intensity in the classic analysis . We will prove a theorem for functional where prove that necessary condition for extreme of functional is the variation of functional is equal to zero. We describe the solution of the equation of Euler with example of application, such as the problem of brachistochrone.

Item Type: Conference or Workshop Item (Poster)
Subjects: Natural sciences > Matematics
Natural sciences > Physical sciences
Divisions: Faculty of Computer Science
Depositing User: Aleksandra Risteska
Date Deposited: 30 Sep 2015 08:44
Last Modified: 03 Mar 2017 08:52
URI: http://eprints.ugd.edu.mk/id/eprint/13886

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