Related papers: Dirac Structures in Vakonomic Mechanics
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we…
In this paper, we present a detailed review/analysis of the Dirac quantisation of Hamiltonian systems with constraints. To this end, we use, as a guide, the physical example provided by the dynamics of a solid ball rolling, without…
We develop a noncommutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous…
We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference…
A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients required for the…
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
We consider nonholonomic systems whose configuration space is the central extension of a Lie group and have left invariant kinetic energy and constraints. We study the structure of the associated Euler-Poincare-Suslov equations and show…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
We propose and study the properties of a non-linear electrodynamics that emerges inspired on the physics of Dirac materials. This new electrodynamic model is an extension of the one-loop corrected non-linear effective Lagrangian computed in…
A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of…
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…
Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The…
In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \emph{Fuzzy Dynamics} of…
The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for…