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English version of abstract:  The dynamic optimization problems treated by the calculus of variations areusually solved with the help of the 2nd order Euler-Lagrange differentialequations. These equations are, generally speaking, nonlinear, and very hard tosolve. One way to address the problem is to obtain conservation laws of lowerorder than those of the corresponding Euler-Lagrange equations. While inPhysics and Economics the question of existence of conservation laws is treatedin a rather natural way, because the application itself suggest theconservation laws (e.g., conservation of energy, income/health law), from astrictly mathematical point of view, given a problem of the calculus ofvariations, it is not obvious how one might derive a conservation law or, forthat matter, if it even has a conservation law. The question we address is thusto develop computational facilities, based on a systematic method, whichpermits to identify functionals that have conservation laws. The central resultwe use is the celebrated Noether's theorem. This theorem links conservationlaws with the invariance properties of the problem (with symmetries), andprovides an algorithm for finding conservation laws. Thus the problem isreduced to the one of finding the variational symmetries. We show how aComputer Algebra System can help to find the symmetries and the conservationlaws in the calculus of variations. Several illustrative examples are given.Comment: 20 pages, in Portuguese. Partially presented at XXVII CNMAC  (Brazilian Congress of Applied Mathematics and Computation), FAMAT/PUCRS,  Porto Alegre, RS, Brasil, 13-16 September 2004. Supported by the program  PRODEP III/5.3/2003 and the R&D unit CEOC of the University of Aveir

Computação Algébrica no Cálculo das Variações: Determinação de Simetrias e Leis de Conservação