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arXiv · 1811.04693

Variational and Optimal Control Approaches for the Second-Order Herglotz Problem on Spheres

L. Machado·L. Abrunheiro·N. Martins
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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.

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L. Machado, L. Abrunheiro, N. Martins. 2018-11-12. Variational and Optimal Control Approaches for the Second-Order Herglotz Problem on Spheres. https://doi.org/10.1007/s10957-018-1424-0

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