Related papers: Noether's theorem in classical mechanics revisited
Two applications of the Noether method for fluids and plasmas are presented based on the Euler-Lagrange and Euler-Poincare variational principles, which depend on whether the dynamical fields are to be varied independently or not,…
The aim of this paper is twofold: First, we give a formal introduction to the basics of the mathematical framework of classical mechanics. Along the way, we prove a Hamiltonian and a Lagrangian version of Noether's Theorem, an important…
For difference variational problems on lattice, this paper presents a relation between divergence variational symmetries and conservation laws for the associated Euler-Lagrange system provided by Noether's theorem. This hence inspires us to…
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 the framework of the classical Maxwell-Lorentz electrodynamics the energy conservation law is reconsidered.
Conservation laws related to the gauge invariance of Lagrangians and Euler-Lagrange operators in finite and infinite order Lagrangian formalisms are analyzed.
This paper mainly contributes to the extension of Noether's theorem to differential-difference equations. For that purpose, we first investigate the prolongation formula for continuous symmetries, which makes a characteristic representation…
In this article, it is suggested that a pedagogical point of departure in the teaching of classical mechanics is the Liouville theorem. The theorem is interpreted to define the condition that describe the conservation of information in…
A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…
We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as well as the discrete one and corrects a previous statement of…
This paper provides a modern presentation of Noether's theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close…
In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we…
This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand…
The irreversibility of the dynamics of the conservative systems on example of hard disks and potentially of interacting elements is investigated in terms of laws of classical mechanics. The equation of the motion of interacting systems and…
We will give several reduction theorems for Noether's problem.
We give the generalization of a recent variational formulation for nonconservative classical mechanics, for fermionic and sypersymmetric systems. Both cases require slightly modified boundary conditions. The supersymmetric version is given…
The direct method based on the definition of conserved currents of a system of differential equations is applied to compute the space of conservation laws of the (1+1)-dimensional wave equation in the light-cone coordinates. Then Noether's…
In the present work foundations of the law of the energy conservation and the introduction of particles in the classical electrodynamics are discussed. We pay attention to a logic error which takes place at an interpretation of the…
Noether's first and second theorems both imply conserved currents that can be identified as an energy-momentum tensor (EMT). The first theorem identifies the EMT as the conserved current associated with global spacetime translations, while…
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…