Related papers: Hamilton-Jacobi approach to Berezinian singular sy…
In this work we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the…
We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and…
Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) ${\it…
In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems and present some examples. Additionally, we present a method for the…
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…
The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence…
We introduce a version of the Hamiltonian formalism based on the Clairaut equation theory, which allows us a self-consistent description of systems with degenerate (or singular) Lagrangian. A generalization of the Legendre transform to the…
A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those…
In this paper, the theory of the fractional singular Lagrangian systems is investigated with second order derivatives. The fractional quantization for these systems is examined using the WKB approximation. The Hamilton Jacobi treatment can…
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…
We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the…
In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of $TT^*Q$…
We prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual…
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…
A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…
We discuss the Hamilton-Jacobi formalism for brane gravity described by the Regge-Teitelboim model, in higher co-dimension. Being originally a second-order in derivatives singular theory, we analyzed its constraint structure by identifying…
In this article we provide a Hamilton-Jacobi formalism in locally conformally symplectic manifolds. Our interest in the Hamilton-Jacobi theory comes from the suitability of this theory as an integration method for dynamical systems, whilst…
The Hamilton-Jacobi formalism for a geodetic brane-like universe described by the Regge-Teitelboim model is developed. We focus on the description of the complete set of Hamiltonians that ensure the integrability of the model in addition to…