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We analyse the constraint structure of the Background Field model for three dimensional gravity including a cosmological term via the Hamilton-Jacobi formalism. We find the complete set of involutive Hamiltonians that assures the…

High Energy Physics - Theory · Physics 2015-09-23 N. T. Maia , B. M. Pimentel , C. E. Valcárcel

We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a…

Mathematical Physics · Physics 2011-08-15 Tomoki Ohsawa , Oscar E. Fernandez , Anthony M. Bloch , Dmitry V. Zenkov

This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…

Mathematical Physics · Physics 2022-05-03 Manuel de León , Manuel Lainz , Asier López-Gordón

A hybrid system is a system whose dynamics is given by a mixture of both continuous and discrete transitions. In particular, these systems can be utilised to describe the dynamics of a mechanical system with impacts. Based on the approach…

Mathematical Physics · Physics 2024-08-21 Leonardo Colombo , Manuel de León , María Emma Eyrea Irazú , Asier López-Gordón

A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new…

In recent years it has been shown for hard sphere gas that, by retaining the correlation information, dynamical fluctuation and large deviation of empirical measure around Boltzmann equation could be proved, in addition to the classical…

Analysis of PDEs · Mathematics 2024-09-05 Chenjiayue Qi

Reduction theory has played a major role in the study of Hamiltonian systems. On the other hand, the Hamilton-Jacobi theory is one of the main tools to integrate the dynamics of certain Hamiltonian problems and a topic of research on its…

Mathematical Physics · Physics 2015-09-02 Manuel de León , David Martín de Diego , Miguel Vaquero

Recently, M. de Le\'on el al. ([9]) have developed a geometric Hamilton-Jacobi theory for Classical Field Theories in the setting of multisymplectic geometry. Our purpose in the current paper is to establish the corresponding…

Mathematical Physics · Physics 2016-02-17 Cédirc M. Campos , Manuel de León , David Martín de Diego , Miguel Vaquero

In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-called \v{C}aplygin systems.

Mathematical Physics · Physics 2007-11-07 D. Iglesias , M. de Leon , D. Martin de Diego

We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and…

Optimization and Control · Mathematics 2011-08-15 Tomoki Ohsawa , Anthony M. Bloch , Melvin Leok

The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…

General Physics · Physics 2012-05-14 V. M. Somsikov

In this paper, we present a generalization of a Hamilton--Jacobi theory to higher order implicit differential equations. We propose two different backgrounds to deal with higher order implicit Lagrangian theories: the Ostrogradsky approach…

Mathematical Physics · Physics 2020-02-19 O. Esen , M. de León , C. Sardón

A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…

General Relativity and Quantum Cosmology · Physics 2017-05-24 Claudio Cremaschini , Massimo Tessarotto

In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton-Jacobi method: one begins with the 2-body Hamilton equations, performs a canonical transformation to the orbital elements, and obtains…

Astrophysics · Physics 2009-11-07 Michael Efroimsky , Peter Goldreich

Gauge invariance of scalar perturbations is studied together with the associated equations of motion. Extending methods developed in the framework of hamiltonian General Relativity, the Hamilton-Jacobi equation is investigated into the…

General Relativity and Quantum Cosmology · Physics 2012-11-01 Thomas Cailleteau , Aurelien Barrau

The Hamilton-Jacobi theory of Classical Mechanics can be extended in a novel manner to systems which are fuzzy in the sense that they can be represented by wave functions. A constructive interference of the phases of the wave functions then…

General Physics · Physics 2007-05-23 B. G. Sidharth

The constrained filed system, the scalar field coupled to two flavours of fermions through Yukawa couplings, is treated by using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many…

General Physics · Physics 2025-06-17 Walaa I. Eshraim

We introduce a new machinery to study the large time behavior for general classes of Hamilton--Jacobi type equations, which include degenerate parabolic equations and weakly coupled systems. We establish the convergence results by using the…

Analysis of PDEs · Mathematics 2013-10-30 Filippo Cagnetti , Diogo Gomes , Hiroyoshi Mitake , Hung Tran

We intend to analyse the constraint structure of Teleparallelism employing the Hamilton-Jacobi formalism for singular systems. This study is conducted without using an ADM 3+1 decomposition and without fixing time gauge condition. It can be…

General Relativity and Quantum Cosmology · Physics 2010-11-11 B. M. Pimentel , P. J. Pompeia , J. F. da Rocha-Neto

The Hamilton-Jacobi analysis for gravity without dynamics is performed. We report a detailed analysis where the complete set of Hamilton-Jacobi constraints, the characteristic equations and the gauge transformations of the theory are found.…

General Relativity and Quantum Cosmology · Physics 2019-05-01 Alberto Escalante , I. Vallejo-Fabila