  English version of abstract:
  The dynamic optimization problems treated by the calculus of variations are
usually solved with the help of the 2nd order Euler-Lagrange differential
equations. These equations are, generally speaking, nonlinear, and very hard to
solve. One way to address the problem is to obtain conservation laws of lower
order than those of the corresponding Euler-Lagrange equations. While in
Physics and Economics the question of existence of conservation laws is treated
in a rather natural way, because the application itself suggest the
conservation laws (e.g., conservation of energy, income/health law), from a
strictly mathematical point of view, given a problem of the calculus of
variations, it is not obvious how one might derive a conservation law or, for
that matter, if it even has a conservation law. The question we address is thus
to develop computational facilities, based on a systematic method, which
permits to identify functionals that have conservation laws. The central result
we use is the celebrated Noether's theorem. This theorem links conservation
laws with the invariance properties of the problem (with symmetries), and
provides an algorithm for finding conservation laws. Thus the problem is
reduced to the one of finding the variational symmetries. We show how a
Computer Algebra System can help to find the symmetries and the conservation
laws in the calculus of variations. Several illustrative examples are given.
