Related papers: Noether conservation laws in classical mechanics
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 work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system…
We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems [F. Samm\"uller…
In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on…
We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine…
Flows of one-dimensional continuum in Lagrangian coordinates are studied in the paper. Equations describing these flows are reduced to a single Euler-Lagrange equation which contains two undefined functions. Particular choices of the…
In the process of calculating Noether's conservation laws, two sets of integration by parts are performed. Here it is shown why the boundary terms from the first set of integration by parts vanish.
Gravitational theories invariant under transverse diffeomorphisms and Weyl transformations have the same classical solutions as the corresponding fully diffeomorphism invariant theories. However, they solve some of the problems related to…
We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and…
Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and…
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…
The first and second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of…
E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished…
We introduce an generalized action functional describing the equations of motion and the variational equations for any Lagrangian system. Using this novel scheme we are able to generalize Noether's theorem in such a way that to any…
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate…
We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic approach. In both classical and quantum mechanics, observables…
In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using…
A Noether-enhanced Legendre transformation from Lagrange densities to energy-momentum tensors is developed into an alternative framework for formulating classical field equations. This approach offers direct access to the Hamiltonian while…