Related papers: Hamilton-Jacobi formulation for singular systems w…
The 2-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for…
An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…
The Hamilton--Jacobi formalism generalized to 2--dimensional field theories according to Lepage's canonical framework is applied to several covariant real scalar fields, e.g. massless and massive Klein--Gordon, Sine--Gordon, Liouville and…
Following the random approach of Mitake, Siconolfi,Tran and Yamada, we define a Lax--Oleinik formula adapted to evolutive weakly coupled systems of Hamilton--Jacobi equations. It is reminiscent of the corresponding scalar formula, with the…
We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a bounded domain with oblique boundary conditions. These equations appear naturally in…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
The problem of the motion of a charged particle in an electric dipole field is used to illustrate that the Hamilton-Jacobi method does not necessarily give all solutions to the equations of motion of a mechanical system. The mathematical…
In this paper, we present and analyse a class of "filtered" numerical schemes for second order Hamilton-Jacobi-Bellman equations. Our approach follows the ideas introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the…
In a recent paper by Ibragimov [N. H. Ibragimov, Invariant Lagrangians and a new method of integration of nonlinear equations, J. Math. Anal. Appl. 304 (2005) 212--235] a method was presented in order to find Lagrangians of certain…
We present a method for the Hamiltonian formulation of field theories that are based on Lagrangians containing second derivatives. The new feature of our formalism is that all four partial derivatives of the field variables are initially…
We consider the Dirac equations in polar form proving that they can equivalently be re-configured into a system of equations consisting of derivatives of the velocity density plus the Hamilton-Jacobi equation, giving the momentum in terms…
It is shown that a chain of closed systems of first order ordinary differential equations describing the evolution of moments can be constructed using the Jacobi equation. It is shown that Wronsky determinants for fundamental matrices of…
The most common physical formalisms are the Lagrangian formalism and the Hamiltonian formalism. From the superficial point of view, they are one and the same, but rewritten in other terms. However, it seems that the Hamiltonian formalism…
The Hamilton-Jacobi equation (HJE) is one of the most elegant approach to Lagrangian systems such as geometrical optics and classical mechanics, establishing the duality between trajectories and waves and paving the way naturally for the…
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.
Most of the laws of Nature involve derivatives up to the second order. Ostrogradski was the first to seek a formulation of the equations of higher-order derivatives. He extended Hamilton's equations by considering Lagrangians that depend on…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
We extend the classical Landesman-Lazer results to the setting of second order Hamilton-Jacobi-Bellman equations. A number of new phenomena appear.
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of…
We prove that a Hamilton-Jacobi equation in 1D with periodic forcing has a set of generalized solutions such that each solution is a sum of linear and continuous periodic functions; we also give a condition of uniqueness of this solution in…