International Journal of Mathematics Trends and Technology
Volume 57 | Number 5 | Year 2018 | Article Id. IJMTT-V57P541 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P541
Variational calculus studied methods for finding maximum and minimum values of functional. It has its inception in 1696 yearby 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 theoremfor 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 Eulerwith example of application, such as the problem of brachistochrone.
[ 1 ] Assoc. Dr. B. Златанов - metric spaces;
[ 2 ] L.Э.Эльсгольц - ДИФФЕРЕНЦИАЛЬНЫЕ equations AND ВАРИАЦИОННОЕ ИСЧИСЛЕНИЕ;
[ 3] Russak I.B. - Calculus of variations (MA4311, 1996);
[ 4] brunt B. - The calculus of variations (ISBN 0387402470), Springer, 2004);
[ 5] Byerly W. - introduction to the calculus of variations (Cambridge, 1917).
Aleksandra Risteska, "Application of Fundamental Lemma of Variational Calculus to the Problem for the Brachistochrone," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 5, pp. 296-302, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P541
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