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Generalized Hamilton-Jacobi equations for nonholonomic dynamics [PDF]
Journal of Mathematical Physics, 2004 Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints.
Kosmol P. +7 more
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On controlled Hamilton and Hamilton–Jacobi differential equations of higher-order [PDF]
Scientific Reports, 2022 In this paper, we investigate the nonlinear dynamics associated with controlled Lagrangians involving higher-order derivatives. More precisely, we establish the controlled higher-order Hamilton ordinary differential equations (ODEs) and Hamilton–Jacobi ...
Savin Treanţă +2 more
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Hamiltonian approach to GR – Part 1: covariant theory of classical gravity
European Physical Journal C: Particles and Fields, 2017 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 Hamilton–Jacobi theory ...
Claudio Cremaschini, Massimo Tessarotto
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Hamilton–Jacobi equations [PDF]
, 2010 In this chapter we discuss numerical methods for the solution of general Hamilton-Jacobi equations of the form $${\phi _t} + H\left( {\nabla \phi } \right) = 0$$ (5.1) where H can be a function of both space and time. In three spatial dimensions, we can write $${\phi _t} + H\left( {{\phi _x},{\phi _y},{\phi _z}} \right) = 0$$ (5.2 ...
Stanley Osher, Ronald Fedkiw
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Mathematics in Engineering, 2023 In recent years there has been intense interest in the vanishing discount problem for Hamilton-Jacobi equations. In the case of the scalar equation, B. Ziliotto has recently given an example of the Hamilton-Jacobi equation having non-convex Hamiltonian ...
Hitoshi Ishii
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Existence of solutions to contact mean-field games of first order
Advanced Nonlinear Studies, 2022 This paper deals with the existence of solutions of a class of contact mean-field game systems of first order consisting of a contact Hamilton-Jacobi equation and a continuity equation.
Hu Xiaotian, Wang Kaizhi
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The Quantum Hamilton–Jacobi Equation and the Link Between Classical and Quantum Mechanics
Quanta, 2022 We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton–Jacobi equation.
Mario Fusco Girard
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Hamilton-Jacobi approach to Berezinian singular systems [PDF]
, 1997 In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra.
B.M. Pimentel +17 more
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Quantum Hamilton-Jacobi Equation [PDF]
Physical Review Letters, 1998 The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the generating function of a canonical transformation that maps any quantum system to a system with a vanishing ...
openaire +2 more sources