Related papers: On Hamiltonian continuum mechanics
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
We consider a geometric framework for analytical mechanics with external forces. Four versions of this framework are considered. A variational principle with boundary terms and external forces.The second and the third versions are the…
Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem…
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are…
The goal of this paper is to present Euler-Lagrange and Hamiltonian equations on R2n which is a model of para-Kaehlerian manifolds of constant J-sectional curvature. In conclusion, some differential geometrical and physical results on the…
We propose a new approach in Lagrangian formalism for studying the fluid dynamics on noncommutative space. Starting with the Poisson bracket for single particle, a map from canonical Lagrangian variables to Eulerian variables is constructed…
The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…
In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical…
The dynamic of a classical system can be expressed by means of Poisson brackets. In this paper we generalize the relation between the usual non covariant Hamiltonian and the Poisson brackets to a covariant Hamiltonian and new brackets in…
The present lecture notes address three columns on which the Lagrangian perturbation approach to cosmological dynamics is based: 1. the formulation of a Lagrangian theory of self--gravitating flows in which the dynamics is described in…
When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…
We demonstrated that classical mechanics have, besides the well known quantum deformation, another deformation -- so called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit $h\to 0$ not only of the…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…
In the framework of Timoshenko beam, the material parameters are inherently prescribed on the material moving frame. In this regard, we derive the strong and weak formulations of the dynamics under finite transformation in Lagrangian…
Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…