Applying the fundamental lemma of variational calculus to the problem of the smallest surfaces in rotation

Risteska, Aleksandra and Gicev, Vlado (2014) Applying the fundamental lemma of variational calculus to the problem of the smallest surfaces in rotation. In: IInternational Conference on Information Technology and Development of Education ITRO 2014, 27 June 2014, Zrenjanin, Republika Srbija.

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Abstract

Variational calculus studies methods for finding maximum and minimum values of functional. It has its inception in 1696 by work of 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 B for the least time. In functional analysis variational calculus takes the same space, as well as theory of maximum and minimum intensity in the classic analysis. We use and prove the theorem for functional where we prove that necessary condition for extreme of functional is the variation of functional to be equal to zero.We have simplified the received necessary condition for extreme and prove so-called, the main lemma of variational calculus. At least we describe private case in the solution of the equation of Euler and give an example of application, such asthe problem of the smallest surfaces in rotation.

Item Type: Conference or Workshop Item (Poster)
Subjects: Natural sciences > Matematics
Divisions: Faculty of Computer Science
Depositing User: Aleksandra Risteska
Date Deposited: 02 Jul 2014 14:09
Last Modified: 02 Jul 2014 14:09
URI: http://eprints.ugd.edu.mk/id/eprint/10377

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