scholarly journals Noether's theorem for higher-order variational problems of Herglotz type

2015 ◽  
Author(s):  
Delfim Torres ◽  
Natália Martins ◽  
Simão P. S. Santos
Keyword(s):  
Variational Problems ◽  
Higher Order ◽  
Noether’S Theorem ◽  
Noether's Theorem

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 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.

scholarly journals HIGHER-ORDER NOETHER SYMMETRIES IN k-SYMPLECTIC HAMILTONIAN FIELD THEORY

2013 ◽  
Vol 10 (08) ◽  
pp. 1360013
Author(s):  
NARCISO ROMÁN-ROY ◽  
MODESTO SALGADO ◽  
SILVIA VILARIÑO
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Vector Fields ◽  
Higher Order ◽  
Field Theories ◽  
Noether Symmetries ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Infinitesimal Transformations

For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by some kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of suitable generalizations of Noether's theorem.

scholarly journals Composition functionals in higher order calculus of variations and Noether's theorem

2021 ◽  
pp. 1-18
Author(s):  
Gastão S. F. Frederico ◽  
J. Vanterler da C. Sousa ◽  
Ricardo Almeida
Keyword(s):  
Calculus Of Variations ◽  
Higher Order ◽  
Noether’S Theorem ◽  
Noether's Theorem

Noether’s Symmetries and Its Inverse for Fractional Logarithmic Lagrangian Systems

2019 ◽  
Vol 7 (1) ◽  
pp. 90-98 ◽  
Author(s):  
Jun Jiang ◽  
Yuqiang Feng ◽  
Shuli Xu
Keyword(s):  
Variational Problems ◽  
Conserved Quantity ◽  
Inverse Theorem ◽  
Lagrangian Systems ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Hamilton Principle ◽  
Fractional Variational Problems

Abstract In this paper, Noether’s theorem and its inverse theorem are proved for the fractional variational problems based on logarithmic Lagrangian systems. The Hamilton principle of the systems is derived. And the definitions and the criterions of Noether’s symmetry and Noether’s quasi-symmetry of the systems based on logarithmic Lagrangians are given. The intrinsic relation between Noether’s symmetry and the conserved quantity is established. At last an example is given to illustrate the application of the results.

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.

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