Related papers: Complex Lagrangian dynamics
This work presents the basic elements of the formalism involved in the treatment of Hamiltonian dynamical systems with symmetry and the geometrical description of collective motion.
Fractional classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented for the fractional classical mechanics.…
We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
New method of quantization is presented. It is based on classical Newton-Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is…
In this note we present invariant formulation of the d'Alambert principle and classical time-dependent Lagrangian mechanics with holonomic constraints from the perspective of moving frames.
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 consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…
Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…
This study presents standard Cliffordian Kaehler analogue of Lagrangian mechanics. Also, the some geometric and physical results related to the standard Cliffordian Kaehler dynamical systems are given.
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian…
In this paper, the possibility to construct a path integral formalism by using the Hubbard operators as field dynamical variables is investigated. By means of arguments coming from the Faddeev-Jackiw symplectic Lagrangian formalism as well…
In the extended Lagrange formalism of classical point dynamics, the system's dynamics is parametrized along a system evolution parameter $s$, and the physical time $t$ is treated as a \emph{dependent} variable $t(s)$ on equal footing with…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
A detailed program is proposed in the Lagrangian formalism to investigate the dynamical behavior of a theory with singular Lagrangian. This program goes on, at different levels, parallel to the Hamiltonian analysis. In particular, we…
We give a formulation of classical mechanics in the language of operators acting on a Hilbert space. The formulation given comes from a unitary irreducible representation of the Galilei group that is compatible with the basic postulates of…
In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to…
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with…