scholarly journals Effects of constraints on Noether symmetries and conserved quantities in a Birkhoffian system

2004 ◽  
Vol 53 (8) ◽  
pp. 2419
Author(s):  
Zhang Yi ◽  
Mei Feng-Xiang
Keyword(s):  
Conserved Quantities ◽  
Noether Symmetries ◽  
Birkhoffian System

scholarly journals Perturbation to Noether Symmetries and Adiabatic Invariants for Birkhoffian Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Yi Zhang
Keyword(s):  
Fractional Integral ◽  
Conservative System ◽  
Dynamical Model ◽  
Lagrangian System ◽  
Adiabatic Invariants ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Small Disturbance ◽  
Birkhoffian System ◽  
Special Cases

Based on El-Nabulsi dynamical model for a non-conservative system, the problem of perturbation to Noether symmetries and adiabatic invariants of a Birkhoffian system under the action of a small disturbance is proposed and studied. Firstly, the El-Nabulsi-Pfaff variational problem from extended exponentially fractional integral is presented and the El-Nabulsi-Birkhoff equations are established. Secondly, the definitions and the criterions criteria of the Noether symmetric transformations and quasisymmetric transformations of the Birkhoffian system are given, and the Noether theorems of the system are established, which reveal the inner relationship between the Noether symmetries and the conserved quantities. Thirdly, the perturbation of Noether symmetries under a small disturbance is studied, and corresponding adiabatic invariants are obtained. As special cases, the deductions in nonconservative Hamiltonian system and nonconservative Lagrangian system and standard Birkhoffian system are given. At the end of the paper, the case known as Hojman-Urrutia problem is discussed to investigate the Noether symmetries and the adiabatic invariants, the perturbation to Noether symmetries and the adiabatic invariants under El-Nabulsi dynamical model.

scholarly journals Noether’s theorems for the relative motion systems on time scales

2018 ◽  
Vol 3 (2) ◽  
pp. 513-526
Author(s):  
Sheng-nan Gong ◽  
Jing-li Fu
Keyword(s):  
Time Scales ◽  
Relative Motion ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Hamilton’S Principle ◽  
Lagrange Equations ◽  
Hamilton's Principle ◽  
Generalized Coordinates ◽  
Delta Derivatives ◽  
Infinitesimal Transformations

AbstractThis paper propose Noether symmetries and the conserved quantities of the relative motion systems on time scales. The Lagrange equations with delta derivatives on time scales are presented for the system. Based upon the invariance of Hamilton action on time scales, under the infinitesimal transformations with respect to the time and generalized coordinates, the Hamilton’s principle, the Noether theorems and conservation quantities are given for the systems on time scales. Lastly, an example is given to show the application the conclusion.

Noether symmetries and anisotropic universe models in f(R, T) gravity

2017 ◽  
Vol 32 (26) ◽  
pp. 1750136 ◽  
Author(s):  
M. Sharif ◽  
Iqra Nawazish
Keyword(s):  
Cosmological Parameters ◽  
Graphical Analysis ◽  
Momentum Tensor ◽  
Anisotropic Universe ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Exponential Expansion ◽  
Symmetry Generators ◽  
Dust Distribution ◽  
Universe Models

This paper investigates the existence of Noether symmetries of some anisotropic homogeneous universe models in non-minimally coupled f(R, T) gravity (R and T represent Ricci scalar and trace of the energy–momentum tensor). We evaluate symmetry generators and the corresponding conserved quantities for two models of this theory admitting direct and indirect non-minimal curvature–matter coupling. We also discuss exact solutions for dust as well as non-dust matter distribution and study the physical behavior of some cosmological parameters through these solutions. For dust distribution, the exact solution corresponds to power-law expansion and Einstein universe while exponential expansion appears for non-dust matter. The graphical analysis of these solutions and cosmological parameters provide consistent results with recent observations about accelerated cosmic expansion. We conclude that Noether symmetry generators and conserved quantities exist for both models.

Conservation laws corresponding to the Noether symmetries of the geodetic Lagrangian in spherically symmetric spacetimes

2017 ◽  
Vol 26 (05) ◽  
pp. 1741006 ◽  
Author(s):  
Bismah Jamil ◽  
Tooba Feroze
Keyword(s):  
Conservation Laws ◽  
Noether Symmetry ◽  
Complete List ◽  
Spherically Symmetric ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes

In this paper, we present a complete list of spherically symmetric nonstatic spacetimes along with the generators of all Noether symmetries of the geodetic Lagrangian for such metrics. Moreover, physical and geometrical interpretations of the conserved quantities (conservation laws) corresponding to each Noether symmetry are also given.

scholarly journals Variational principles and symmetries on fibered multisymplectic manifolds

2016 ◽  
Vol 24 (2) ◽  
pp. 137-152 ◽  
Author(s):  
Jordi Gaset ◽  
Pedro D. Prieto-Martínez ◽  
Narciso Román-Roy
Keyword(s):  
Variational Principles ◽  
Variational Calculus ◽  
Field Theories ◽  
Fiber Bundles ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Geometric Framework ◽  
Gauge Symmetries ◽  
Special Cases ◽  
Standard Techniques

Abstract The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multi-symplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.

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