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Symbolic Computation in the Calculus of Variations: Determination of Symmetries and Conservation Laws (in Portuguese)
Paulo D. F. Gouveia, Delfim F. M. Torres
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 e…
A Noether Theorem on Unimprovable Conservation Laws for Vector-Valued Optimization Problems in Control Theory
Delfim F. M. Torres
We obtain a version of Noether's invariance theorem for optimal control problems with a finite number of cost functionals. The result is obtained by formulating E. Noether's result…
On the Noether Invariance Principle for Constrained Optimal Control Problems
Delfim F. M. Torres
We obtain a generalization of Noether's invariance principle for optimal control problems with equality and inequality state-input constraints. The result relates the invariance pr…
Consecutive, Reversed, Mirror, and Symmetric Smarandache Sequences of Triangular Numbers
Delfim F. M. Torres, Viorica Teca
We use the Maple system to check the investigations of S. S. Gupta regarding the Smarandache consecutive and the reversed Smarandache sequences of triangular numbers [Smarandache N…
Newton's aerodynamic problem in media of chaotically moving particles
Alexander Yu. Plakhov, Delfim F. M. Torres
We study the problem of minimal resistance for a body moving with constant velocity in a rarefied medium of chaotically moving point particles, in Euclidean space R^d. The particle…
Optimal Control of Newton-Type Problems of Minimal Resistance
Delfim F. M. Torres, Alexander Yu. Plakhov
We address Newton-type problems of minimal resistance from an optimal control perspective. It is proven that for Newton-type problems the Pontryagin maximum principle is a necessar…
Two-Dimensional Problems of Minimal Resistance in a Medium of Positive Temperature
Alexander Yu. Plakhov, Delfim F. M. Torres
We study the Newton-like problem of minimal resistance for a two-dimensional body moving with constant velocity in a homogeneous rarefied medium of moving particles. The distributi…