相关论文: The structure of time and inertial forces in Lagra…

We consider the Euler equations of incompressible inviscid fluid dynamics. We discuss a variational formulation of the governing equations in Lagrangian coordinates. We compute variational symmetries of the action functional and generate…

The usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a…

The phenomenon of local dynamical inhomogeneity of time is predicted, which implies that the course of time along the trajectory of motion of a particle in the inertial reference frames moving relative to each other depends on the state of…

We consider the ambiguity associated with the choice of clock in time reparameterization invariant theories. This arbitrariness undermines the goal of prescribing a fixed set of physical laws, since a change of time variable can completely…

Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but…

The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…

We make use of the Lagrangian description of fluid motion to highlight certain features in the context of spacetime geometry as emergent phenomena in fluid systems. We find by using Lagrangian Perturbation Theory (LPT), that not all kind of…

A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or…

It is postulated there is not a precise static instant in time underlying a dynamical physical process at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined.…

Time directions are not invariant in conventional thermodynamics. We broadly follow ideas of Ludwig Boltzmann and investigate implications of postulating time-directional invariance in thermodynamics. In this investigation, we require that…

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…

We analyze the relation of the notion of a pluri-Lagrangian system, which recently emerged in the theory of integrable systems, to the classical notion of variational symmetry, due to E. Noether. We treat classical mechanical systems and…

Fractional equations appear in the description of the dynamics of various physical systems. For Lagrangian systems, the embedding theory developped by Cresson ["Fractional embedding of differential operators and Lagrangian systems", J.…

Time variation of fundamental constants would not be surprising in the framework of theories involving extra dimensions. The variation of any one constant is likely to be correlated with variations of others in a pattern that is diagnostic…

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…

The notions of time in the theories of Newton and Einstein are reviewed so that certain of their assumptions are clarified. These assumptions will be seen as the causes of the incompatibility between the two different ways of understanding…

We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integrable lattice systems. We derive the multi-time Euler…

Lagrangian coherent structures are effective barriers, sticky regions, that separate phase space regions of different dynamical behavior. The usual way to detect such structures is via finite-time Lyapunov exponents. We show that similar…

Lagrangian properties obtained from a Particle Tracking Velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian…

The logic--linguistic structure of quantum physics is analysed. The role of formal systems and interpretations in the representation of nature is investigated. The problems of decidability, completeness, and consistency can affect quantum…