Non-Noether symmetries and conserved quantities of nonconservative dynamical systems

2003 ◽  
Vol 317 (3-4) ◽  
pp. 255-259 ◽  
Author(s):  
Jing-Li Fu ◽  
Li-Qun Chen
Keyword(s):  
Dynamical Systems ◽  
Conserved Quantities ◽  
Noether Symmetries

scholarly journals Non-Noether Symmetries in Singular Dynamical Systems

2001 ◽  
Vol 8 (1) ◽  
pp. 27-32
Author(s):  
G. Chavchanidze
Keyword(s):  
Dynamical Systems ◽  
Conservation Law ◽  
Conserved Quantities ◽  
Noether Symmetries

Abstract The Hojman–Lutzky conservation law establishes a certain correspondence between non-Noether symmetries and conserved quantities. In the present paper the extension of the Hojman–Lutzky theorem to singular dynamical systems is carried out.

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.

scholarly journals New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries

2020 ◽  
Vol 17 (06) ◽  
pp. 2050090 ◽  
Author(s):  
Jordi Gaset ◽  
Xavier Gràcia ◽  
Miguel C. Muñoz-Lecanda ◽  
Xavier Rivas ◽  
Narciso Román-Roy
Keyword(s):  
Dynamical Systems ◽  
Mechanical Systems ◽  
Dissipative Systems ◽  
Conserved Quantities ◽  
Dynamical Equations ◽  
Lagrangian Formulations ◽  
New Form

We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying their equivalence. We define several kinds of symmetries for contact dynamical systems, as well as the notion of dissipation laws, prove a dissipation theorem and give a way to construct conserved quantities. Some well-known examples of dissipative systems are discussed.

Dynamical systems: Approximate Lagrangians and Noether symmetries

2019 ◽  
Vol 16 (10) ◽  
pp. 1950160 ◽  
Author(s):  
Sameerah Jamal
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems ◽  
Variational Principle ◽  
Kinetic Energy ◽  
Equations Of Motion ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Geometric Conditions ◽  
Finite Dimensional ◽  
Second Order Equations

We determine the approximate Noether point symmetries of the variational principle characterizing second-order equations of motion of a particle in a (finite-dimensional) Riemannian manifold. In particular, the Lagrangian comprises of kinetic energy and a potential [Formula: see text], perturbed to [Formula: see text]. We establish a convenient system of approximate geometric conditions that suffices for the computation of approximate Noether symmetry vectors and moreover, simplifies the problem of the effect of higher orders of the perturbation. The general results are applied to several practical problems of interest and we find extra Noether symmetries at [Formula: see text].

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.

Sign in / Sign up

Export Citation Format

Share Document