Variational Principle and Conservation Laws of a Generalized Hyperbolic Lane–Emden System

2018 ◽  
Vol 13 (12) ◽  
Author(s):  
Ben Muatjetjeja ◽  
Tshepo E. Mogorosi
Keyword(s):  
Variational Principle ◽  
Conservation Laws ◽  
Physical Meaning ◽  
Symmetry Analysis ◽  
Noether Symmetry ◽  
Noether Symmetries

This paper aims to perform a complete Noether symmetry analysis of a generalized hyperbolic Lane–Emden system. Several constraints for which Noether symmetries exist are derived. In addition, we construct conservation laws associated with the admitted Noether symmetries. Thereafter, we briefly discuss the physical meaning of the derived conserved vectors.

scholarly journals Noether Symmetries of a Generalized Coupled Lane-Emden-Klein-Gordon-Fock System with Central Symmetry

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 566 ◽  
Author(s):  
B. Muatjetjeja ◽  
S. O. Mbusi ◽  
A. R. Adem
Keyword(s):  
Conservation Laws ◽  
Physical Interpretation ◽  
Symmetry Analysis ◽  
Central Symmetry ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Klein Gordon

In this paper we carry out a complete Noether symmetry analysis of a generalized coupled Lane-Emden-Klein-Gordon-Fock system with central symmetry. It is shown that several cases transpire for which the Noether symmetries exist. Moreover, we derive conservation laws connected with the admitted Noether symmetries. Furthermore, we fleetingly discuss the physical interpretation of the these conserved vectors.

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].

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.

Noether Symmetry Analysis of the Dynamic Euler-Bernoulli Beam Equation

2016 ◽  
Vol 71 (5) ◽  
pp. 447-456 ◽  
Author(s):  
A.G. Johnpillai ◽  
K.S. Mahomed ◽  
C. Harley ◽  
F.M. Mahomed
Keyword(s):  
Conservation Laws ◽  
Power Law ◽  
Numerical Solutions ◽  
Noether Symmetry ◽  
Numerical Code ◽  
Beam Equation ◽  
Noether Symmetries ◽  
Bernoulli Beam ◽  
Symmetry Classification ◽  
Euler Bernoulli Beam

AbstractWe study the fourth-order dynamic Euler-Bernoulli beam equation from the Noether symmetry viewpoint. This was earlier considered for the Lie symmetry classification. We obtain the Noether symmetry classification of the equation with respect to the applied load, which is a function of the dependent variable of the underlying equation. We find that the principal Noether symmetry algebra is two-dimensional when the load function is arbitrary and extends for linear and power law cases. For all cases, for each of the Noether symmetries associated with the usual Lagrangian, we construct conservation laws for the equation via the Noether theorem. We also provide a basis of conservation laws by using the adjoint algebra. The Noether symmetries pick out the special value of the power law, which is –7. We consider the Noether symmetry reduction for this special case, which gives rise to a first integral that is used for our numerical code. For this, we then find numerical solutions using an in-built function in MATLAB called bvp4c, which is a boundary value solver for differential equations that are depicted in five figures. The physical solutions obtained are for the deflection of the beam with an increase in displacement. These are given in four figures and discussed.

scholarly journals Fractional Birkhoffian Mechanics Based on Quasi-Fractional Dynamics Models and Its Noether Symmetry

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Yun-Die Jia ◽  
Yi Zhang
Keyword(s):  
Conservation Laws ◽  
Fractional Order ◽  
Fractional Integral ◽  
Noether Symmetry ◽  
Order Derivative ◽  
Fractional Dynamics ◽  
Noether Symmetries ◽  
Fractional Order Derivative ◽  
Dynamics Models

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 are nonconservative dynamics models proposed by El-Nabulsi, including three cases: extended by Riemann–Liouville fractional integral (abbreviated as ERLFI), extended by exponential fractional integral (abbreviated as EEFI), and extended by periodic fractional integral (abbreviated as EPFI). First, the fractional Pfaff–Birkhoff principles based on quasi-fractional dynamics models are proposed, in which the Pfaff action contains the fractional-order derivative terms, and the corresponding fractional Birkhoff’s equations are obtained. Second, the Noether symmetries and conservation laws of the systems are studied. Finally, three concrete examples are given to demonstrate the validity of the results.

A study of Noether symmetries in LRS Bianchi type V spacetimes

2019 ◽  
Vol 35 (06) ◽  
pp. 2050026 ◽  
Author(s):  
Sumaira Saleem Akhtar ◽  
Tahir Hussain
Keyword(s):  
Conservation Laws ◽  
Lie Algebra ◽  
Bianchi Type ◽  
Noether Symmetry ◽  
Energy Conditions ◽  
Noether Symmetries ◽  
Rotationally Symmetric ◽  
Symmetry Generators ◽  
Type V ◽  
Bianchi Type V

In this paper, we have studied Noether symmetries of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Solving the determining equations of Noether symmetries, it is concluded that the dimension of Noether algebra for these spacetimes is 5, 6, 7, 9, 10, 11 or 17. For all Noether symmetry generators, we have presented the corresponding conservation laws and the Lie algebra. Moreover, some physical implications of the obtained metrics are discussed, which include the study of different energy conditions.

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