Related papers: Open Systems in Classical Mechanics
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
This contribution aims to shed light on mathematical epidemic dynamics modelling from the viewpoint of analytical mechanics. To set the stage, it recasts the basic SIR model of mathematical epidemic dynamics in an analytical mechanics…
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking…
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…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…
The existence of the theory of `twisted cotangent bundles' (symplectic groupoids) allows to study classical mechanical systems which are generalized in the sense that their configurations form a Poisson manifold. It is natural to study from…
Submanifolds of a manifold are described as sections of a certain fiber bundle that enables one to consider their Lagrangian and (polysymplectic) Hamiltonian dynamics as that of a particular classical field theory. In particular, their…
Within the frames of the analytical mechanics the method of the description of dynamics of nonequilibrium systems of potentially interacting elements is develops. The method is based on an opportunity of representation of nonequilibrium…
It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we…
We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such…
In this paper a class of classical Hamiltonian systems is geometrically formulated. This class is such that a Hamiltonian can be written as the sum of a kinetic energy function and a potential energy function. In addition, these energy…
We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged)…
Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. Then it comes to discussing conjectures of whether all primary constraints…
A comparative analysis of two different versions of the Legendre transformation is presented. We provide an almost complete although somewhat superficial review of the geometric background for analytical mechanics. Complete coordinate…
In a fundamental formulation of the quantum mechanics of a closed system such as the universe as a whole, three forms of information are needed to make predictions for the probabilities of alternative time histories of the closed system .…
The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter $\omega(\phi)$.…
We show how to use operators in the description of {\em exchanging processes} often taking place in (complex) classical systems. In particular, we propose a set of rules giving rise to an {\em hamiltonian} operator for such a system $\Sc$,…
In order to diagnose the cause of some defects in the category of canonical hypergroups, we investigate several categories of hyperstructures that generalize hypergroups. By allowing hyperoperations with possibly empty products, one obtains…
We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of…