101 citations · 650 across the 25 of their papers we have counts for
26 papers
Variational and Optimal Control Approaches for the Second-Order Herglotz Problem on Spheres
L. Machado, L. Abrunheiro, N. Martins
The present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere S^n following variational and optimal…
Noether currents for higher-order variational problems of Herglotz type with time delay
Simao P. S. Santos, Natalia Martins, Delfim F. M. Torres
We study, from an optimal control perspective, Noether currents for higher-order problems of Herglotz type with time delay. Main result provides new Noether currents for such gener…
Higher-order variational problems of Herglotz type with time delay
Simao P. S. Santos, Natalia Martins, Delfim F. M. Torres
We study, using an optimal control point of view, higher-order variational problems of Herglotz type with time delay. Main results are higher-order Euler-Lagrange and DuBois-Reymon…
Noether's theorem for higher-order variational problems of Herglotz type
Simao P. S. Santos, Natalia Martins, Delfim F. M. Torres
We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler-Lagrange equation,…
Variational problems for Holderian functions with free terminal point
Ricardo Almeida, Natália Martins
We develop the new variational calculus introduced in 2011 by J. Cresson and I. Greff, where the classical derivative is substituted by a new complex operator called the scale deri…
Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem
Simao P. S. Santos, Natalia Martins, Delfim F. M. Torres
We extend the DuBois-Reymond necessary optimality condition and Noether's first theorem to variational problems of Herglotz type with time delay. Our results provide, as corollarie…