Generalization of the application of a fundamental lemma of variational calculus to revolutionize transportation by using the solution of brachistochrone

Risteska, Aleksandra (2023) Generalization of the application of a fundamental lemma of variational calculus to revolutionize transportation by using the solution of brachistochrone. Balkan Journal of Applied Mathematics and Informatics, VI (1). ISSN 2545-4083

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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 ofthe brachistochrone: to find a curve connecting two points A and B, which does not lie in a vertical, so that theheavy point descends along this curve from position A to reach position B in the shortest time. In functional analysis,variational calculus takes the same space, as well as the theory of maximumand minimumintensity in the classic analysis. We will prove a theorem for functional whereweprove thatthenecessary condition for the extreme of the functional is the variation of functional to beequal to zero. We describe the solution of the equation of Euler with an example of application, such as the problem of brachistochrone, and its generalization that has the potential to completely revolutionize transportation.

Item Type:	Article
Subjects:	Natural sciences > Computer and information sciences Natural sciences > Matematics
Divisions:	Faculty of Computer Science
Depositing User:	Aleksandra Risteska
Date Deposited:	05 Jul 2023 08:04
Last Modified:	05 Jul 2023 08:04
URI:	https://eprints.ugd.edu.mk/id/eprint/32017

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