Symmetries, Conservation Laws and Multipliers via Partial Lagrangians and Noether’s Theorem for Classically Non-Variational Problems

2007 ◽  
Vol 46 (12) ◽  
pp. 3022-3029 ◽  
Author(s):  
D. N. Khan Marwat ◽  
A. H. Kara ◽  
F. M. Mahomed
Keyword(s):  
Conservation Laws ◽  
Variational Problems ◽  
Noether’S Theorem ◽  
Noether's Theorem

Introduction

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Conservation Laws ◽  
Lagrangian Mechanics ◽  
General Introduction ◽  
Noether’S Theorem ◽  
Noether's Theorem

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is included.

scholarly journals Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Jun Jiang ◽  
Yuqiang Feng ◽  
Shougui Li
Keyword(s):  
Fractional Derivative ◽  
Sufficient Conditions ◽  
Variational Problems ◽  
Necessary And Sufficient Conditions ◽  
Optimal Conditions ◽  
Lagrange Equations ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Necessary And Sufficient

In this paper, the necessary and sufficient conditions of optimality for variational problems with Caputo partial fractional derivative are established. Fractional Euler-Lagrange equations are obtained. The Legendre condition and Noether’s theorem are also presented.

scholarly journals Conservation Laws in Physics – Emmy Noether’s Theorem

2014 ◽  
Vol 29 ◽  
pp. 55-61
Author(s):  
Daniela Manolea
Keyword(s):  
Conservation Laws ◽  
Celestial Body ◽  
Practical Importance ◽  
Microscopic Level ◽  
Human Knowledge ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
The World ◽  
Physical Laws ◽  
Practical Impact

The study is explanatory-interpretative and argues the practical character of Physics. It starts from premise that formation of a correct conception of the world begins with the understanding of physics. It is one of the earliest chapters of human knowledge, studying the material world from the microscopic level of the particles to the macroscopic level of the celestial body. As an example for the practical importance of applying the laws of physics take the set of physical laws of conservation, in particular, it explains the practical impact of Emmy Noether's Theorem.

Conservation laws of linear elasticity in stress formulations

2005 ◽  
Vol 461 (2053) ◽  
pp. 99-116 ◽  
Author(s):  
Shaofan Li ◽  
Anurag Gupta ◽  
Xanthippi Markenscoff
Keyword(s):  
Conservation Laws ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Cauchy Stress ◽  
General Boundary Conditions ◽  
Cauchy Stress Tensor ◽  
Equilibrium Equations ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Three Dimensional Elasticity

In this paper, we present new conservation laws of linear elasticity which have been discovered. These newly discovered conservation laws are expressed solely in terms of the Cauchy stress tensor, and they are genuine, non–trivial conservation laws that are intrinsically different from the displacement conservation laws previously known. They represent the variational symmetry conditions of combined Beltrami–Michell compatibility equations and the equilibrium equations. To derive these conservation laws, Noether's theorem is extended to partial differential equations of a tensorial field with general boundary conditions. By applying the tensorial version of Noether's theorem to Pobedrja's stress formulation of three–dimensional elasticity, a class of new conservation laws in terms of stresses has been obtained.

scholarly journals Noether’s theorem for non-smooth extremals of variational problems with time delay

2013 ◽  
Vol 93 (1) ◽  
pp. 153-170 ◽  
Author(s):  
Gastão S.F. Frederico ◽  
Tatiana Odzijewicz ◽  
Delfim F.M. Torres
Keyword(s):  
Time Delay ◽  
Variational Problems ◽  
Noether’S Theorem ◽  
Noether's Theorem

Noether’s theorem for fractional variational problems of variable order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Tatiana Odzijewicz ◽  
Agnieszka Malinowska ◽  
Delfim Torres
Keyword(s):  
Optimality Condition ◽  
Variational Problems ◽  
Time Variable ◽  
Variable Order ◽  
Necessary Optimality Condition ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Fractional Variational Problems ◽  
Derivatives Of

AbstractWe prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether’s theorem without transformation of the independent (time) variable. Considered derivatives of variable order are defined in the sense of Caputo.

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