Open AccessCálculo variacional e aplicações
Author(s) -
Jardel Carpes Meurer,
Lucas Tavares Cardoso,
Glauber Rodrigues de Quadros
Publication year - 2020
Publication title -
ciência e natura
Language(s) - English
Resource type - Journals
eISSN - 2179-460X
pISSN - 0100-8307
DOI - 10.5902/2179460x40596
Subject(s) - maxima and minima , simple (philosophy) , calculus of variations , calculus (dental) , context (archaeology) , mathematics , computer science , mathematical analysis , epistemology , philosophy , geography , medicine , dentistry , archaeology
This paper consists of a brief review and introduction to the main concepts of Classic Variational Calculus. Starting from thedefinitions of the concepts of first and second variation of a functional, we present a mathematically rigorous treatment for theVariational Calculus, establishing necessary and sufficient conditions for obtaining extrema. In this context, the notion of conjugatepoints is introduced, which is fundamental for the classification of weak extrema. Some simple and enlightening examples are dealtwith throughout the paper. Strong extrema are characterized and sufficient conditions for their occurrence are given. The paperconcludes with a brief application to Lagrange mechanics, showing the existence of actions whose stationary points are saddlepoints instead of minima.