Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems
@article{Lazo2019NoetherTF, title={Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems}, author={Matheus J. Lazo and Juilson Paiva and Gast{\~a}o S. F. Frederico}, journal={Nonlinear Dynamics}, year={2019}, pages={1-12} }
In the present work, we formulate a generalization of the Noether Theorem for action-dependent Lagrangian functions. The Noether’s theorem is one of the most important theorems for physics. It is well known that all conservation laws, e.g., conservation of energy and momentum, are directly related to the invariance of the action under a family of transformations. However, the classical Noether theorem cannot be applied to study non-conservative systems because it is not possible to formulate…
8 Citations
A geometric approach to the generalized Noether theorem
- Mathematics
- 2020
We provide a geometric extension of the generalized Noether theorem for scaling symmetries recently presented by Zhang P-M et al (2020 Eur. Phys. J. Plus 135 223). Our version of the generalized…
Generalized nonconservative gravitational field equations from Herglotz action principle
- PhysicsPhysical Review D
- 2022
We present an alternative nonconservative gravitational theory based on the Herglotz variational principle in a fully covariant form. The present model may be seen as an improvement of the theory…
Herglotz's Variational Problem for Non-Conservative System with Delayed Arguments under Lagrangian Framework and Its Noether's Theorem
- MathematicsSymmetry
- 2020
The aim of this paper is to explore Herglotz’s variational problem for a non-conservative system with delayed arguments under Lagrangian framework and its Noether‘s theorem and derive the non-isochronous variation formulas of Hamilton–HerglotZ action containing delayed arguments.
Nonsmooth Herglotz variational principle
- MathematicsArXiv
- 2022
—In this paper, the theory of smooth action-dependent Lagrangian mechanics (also known as contact Lagrangians) is extended to a non-smooth context appropriate for collision problems. In particular,…
Time-scales Herglotz type Noether theorem for delta derivatives of Birkhoffian systems
- MathematicsRoyal Society Open Science
- 2019
Time-scales Herglotz type Noether identity and Noether theorem for delta derivatives of Birkhoffian systems are proposed and proved and shown to be more universal than Hamiltonian or Lagrangian formalism.
From Geometry to Coherent Dissipative Dynamics in Quantum Mechanics
- PhysicsQuantum Reports
- 2021
Starting from the geometric description of quantum systems, we propose a novel approach to time-independent dissipative quantum processes according to which energy is dissipated but the coherence of…
Fractional Birkhoffian Mechanics Based on Quasi-Fractional Dynamics Models and Its Noether Symmetry
- Mathematics
- 2021
This paper focuses on the exploration of fractional Birkhoffian mechanics and its fractional Noether theorems under quasi-fractional dynamics models. The quasi-fractional dynamics models under study…
Noether symmetry and its inverse for dynamical systems with two kinds of nonstandard Lagrangians via quasi-coordinates
- MathematicsIndian Journal of Physics
- 2021
References
SHOWING 1-10 OF 35 REFERENCES
An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems
- Mathematics
- 2018
In this work, we propose an Action Principle for Action-dependent Lagrangian functions by generalizing the Herglotz variational problem to the case with several independent variables. We obtain a…
Noether’s theorem for fractional Herglotz variational principle in phase space
- MathematicsChaos, Solitons & Fractals
- 2019
Action principle for action-dependent Lagrangians toward nonconservative gravity: Accelerating universe without dark energy
- Physics
- 2017
In the present work, we propose an Action Principle for Action-dependent Lagrangians by generalizing the Herglotz variational problem for several independent variables. This Action Principle enables…
Variational problem of Herglotz type for Birkhoffian system and its Noether’s theorems
- Mathematics
- 2017
Herglotz proposed a generalized variational principle through his work on contact transformations and their connections with Hamiltonian systems and Poisson brackets, which provides an effective…
The action principle for dissipative systems
- Mathematics
- 2014
In the present work we redefine and generalize the action principle for dissipative systems proposed by Riewe by fixing the mathematical inconsistencies present in the original approach. In order to…
Generalized variational principle of Herglotz for several independent variables. First Noether-type theorem
- Mathematics
- 2003
This paper extends the generalized variational principle of Herglotz to one with several independent variables and derives the corresponding generalized Euler–Lagrange equations. The extended…
Noether’s Theorem and its Inverse of Birkhoffian System in Event Space Based on Herglotz Variational Problem
- Mathematics
- 2018
Herglotz variational principle, in which the functional is defined by a differential equation, generalizes the classical ones defining the functional by an integral. The principle gives a variational…
Quantum friction in the c‐number picture: The damped harmonic oscillator
- Physics
- 1980
Considering the Lagrangian proposed by Havas, that describes the classical damped motion of a particle, new momentum and position are defined in order to write a Hamiltonian that is subsequently…