Produção Nacional
Cálculo variacional e aplicações
2020; UNIVERSIDADE FEDERAL DE SANTA MARIA; Volume: 42; Linguagem: Inglês
10.5902/2179460x40596
ISSN2179-460X
AutoresJardel Carpes Meurer, Lucas Tavares Cardoso, Glauber Rodrigues de Quadros,
Tópico(s)Dynamics and Control of Mechanical Systems
ResumoThis 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.
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