Paulo D. F. Gouveia, Delfim F. M. Torres, Eugenio A. M. Rocha
Published 2006-04-04Version 1
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 Noether's first integrals, possibly in the presence of nonconservative external forces. As an application, we obtain eight independent first integrals for the sub-Riemannian nilpotent problem (2,3,5,8).
Comments: Presented at the 4th Junior European Meeting on "Control and Optimization", Bialystok Technical University, Bialystok, Poland, 11-14 September 2005. Accepted (24-Feb-2006) to Control & Cybernetics
Journal: Control Cybernet. 35 (2006), no. 4, 831--849.
Symbolic Computation in the Calculus of Variations: Determination of Symmetries and Conservation Laws (in Portuguese)
Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control
Symbolic computation in hyperbolic programming
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