| Popis: |
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. |
