Related papers: Lectures on Classical Mechanics -- A Didactical Ap…
Classical non-relativistic mechanics in a general setting of time-dependent transformations and reference frame changes is formulated in the terms of fibre bundles over the time-axis R. Connections on fibre bundles are the main ingredient…
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…
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…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
This note presents an attempt to provide a conceptual framework for variational formulations of classical physics. Variational principles of physics have all a common source in the {\it principle of virtual work} well known in statics of…
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to…
The aim of this work is to provide a possible philosophical motivation to the variational principles of physics in general and a possible way to unify the axiomatizations of mechanics theories. The leitmotif of this work is a dialectical…
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
The basic concepts of classical mechanics are given in the operator form. Then, the hybrid systems approach, with the operator formulation of both quantum and classical sector, is applied to the case of an ideal nonselective measurement. It…
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…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
Noether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped harmonic oscillator problem with respect to…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
Classical mechanics for individual physical systems and quantum mechanics of non-relativistic particles are shown to be exceptional cases of a generalized dynamics described in terms of maps between two manifolds, the source being…
We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…