Variational and Optimal Control Approaches for the Second-Order Herglotz Problem on Spheres
Differential Geometry
2018-11-13 v1 Optimization and Control
Abstract
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 control approaches. The relation between the Hamiltonian equations and the generalized Euler-Lagrange equations is established. This problem covers some classical variational problems posed on the Riemannian manifold S^n such as the problem of finding cubic polynomials on S^n. It also finds applicability on the dynamics of the simple pendulum in a resistive medium.
Cite
@article{arxiv.1811.04693,
title = {Variational and Optimal Control Approaches for the Second-Order Herglotz Problem on Spheres},
author = {L. Machado and L. Abrunheiro and N. Martins},
journal= {arXiv preprint arXiv:1811.04693},
year = {2018}
}