Non-commutative integrability, exact solvability and the Hamilton–Jacobi theory

Autor: Sergio Grillo

Publikováno v: Analysis and Mathematical Physics. 11

The non-commutative integrability (NCI) is a property fulfilled by some Hamiltonian systems that ensures, among other things, the exact solvability of their corresponding equations of motion. The latter means that an “explicit formula” for the tr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::adb0d8152dad8f99648b97560730ad86
https://doi.org/10.1007/s13324-021-00512-5

Existence of isotropic complete solutions of the Π-Hamilton–Jacobi equation

Autor: Sergio Grillo

Publikováno v: CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET

Consider a symplectic manifold M, a Hamiltonian vector field X and a fibration Π:M→N. Related to these data we have a generalized version of the (time-independent) Hamilton–Jacobi equation: the Π-HJE for X, whose unknown is a section σ:N→M o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::14c9481c3bd3b25ea6d16b8dd33a8e1e
https://www.sciencedirect.com/science/article/pii/S0393044019302256

On the relationship between the energy shaping and the Lyapunov constraint based methods

Autor: Sergio Grillo, Marcela Zuccalli, Leandro Salomone

Publikováno v: Journal of Geometric Mechanics. 9:459-486

In this paper, we make a review of the controlled Hamiltonians (CH) method and its related matching conditions, focusing on an improved version recently developed by D.E. Chang. Also, we review the general ideas around the Lyapunov constraint based (

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::408508eb7b7cebcf92496344b027091f
https://doi.org/10.3934/jgm.2017018

Error analysis of forced discrete mechanical systems

Autor: Sergio Grillo, Javier Fernandez, Sebastián Elías Graiff Zurita

Publikováno v: Journal of Geometric Mechanics. 13:533

The purpose of this paper is to perform an error analysis of the variational integrators of mechanical systems subject to external forcing. Essentially, we prove that when a discretization of contact order $r$ of the Lagrangian and force are used, th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45b797c13319366eb7497c25d317c2d6
https://doi.org/10.3934/jgm.2021017

A Hamilton–Jacobi Theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds

Autor: Sergio Grillo, Edith Padrón

Publikováno v: CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET
Digital.CSIC. Repositorio Institucional del CSIC
instname

29 págs.
In this paper we develop, in a geometric framework, a Hamilton–Jacobi Theory for general dynamical systems. Such a theory contains the classical theory for Hamiltonian systems on a cotangent bundle and recent developments in the fram

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89f9ccc8ed37ddcc6dee766042875bb9
https://www.sciencedirect.com/science/article/pii/S0393044016301760