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We develop a Hamilton-Jacobi theory for singular lagrangian systems in the Skinner-Rusk formalism. Comparisons with the Hamilton-Jacobi problem in the lagrangian and hamiltonian settings are discussed.
The semi-Lagrangian methods with the improved number of one-dimensional advections are proposed for a plasma hybrid model with kinetic ions and mass-less electrons. Two subsystems with mass, momentum, and energy conservation are obtained by…
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…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
In recent years it has been shown that many, and possibly all, integrable systems can be obtained by dimensional reduction of self-dual Yang-Mills. I show how the integrable systems obtained this way naturally inherit bihamiltonian…
A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
We compare Whitham averaging method using Lagrangian and Hamiltonian formalism.
A stochastic dynamics framework for the study of complex systems is presented.
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
This paper is the third of a series on Hamiltonian stationary Lagrangian surfaces. We present here the most general theory, valid for any Hermitian symmetric target space. Using well-chosen moving frame formalism, we show that the equations…
An overview of dynamical systems in accelerator physics is presented with a suggestion of a few issues to be addressed. Also mentioned are a few possible developments in the future. Technical details supporting the views are not presented.
We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
We study certain two-dimensional variational systems, namely pluri-Lagrangian systems on the root lattice $Q(A_{N})$. Here, we follow the scheme which was already used to define two-dimensional pluri-Lagrangian systems on the lattice…
A Lagrangian system with two degrees of freedom is considered. The configuration space of the system is a cylinder. A large class of periodic solutions has been found. The solutions are not homotopy equivalent to each other.
We develop a new, coordinate-free formulation of Hamiltonian mechanics on the dual of a Lie algebroid. Our approach uses a connection, rather than coordinates in a local trivialization, to obtain global expressions for the horizontal and…