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Symbolic Computation of Variational Symmetries in Optimal Control
Paulo D. F. Gouveia, Delfim F. M. Torres, Eugenio A. M. Rocha
We use a computer algebra system to compute, in an efficient way, optimal control variational symmetries up to a gauge term. The symmetries are then used to obtain families of Noet…
Quadratures of Pontryagin Extremals for Optimal Control Problems
Eugenio A. M. Rocha, Delfim F. M. Torres
We obtain a method to compute effective first integrals by combining Noether's principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrabil…
First Integrals for Problems of Calculus of Variations on Locally Convex Spaces
Eugenio A. M. Rocha, Delfim F. M. Torres
The fundamental problem of calculus of variations is considered when solutions are differentiable curves on locally convex spaces. Such problems admit an extension of the Euler-Lag…