Noether symmetries of discrete nonholonomic dynamical systems

Fu, Jing-Li; Chen, Benyong; Chen, Liqun

doi:10.1016/j.physleta.2008.11.039

Cited by 41 publications

(25 citation statements)

References 16 publications

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“…Hence, it is of great significance to study. Up to now many results about Noether theory have been obtained, such as Noether theory based on fractional models, see [7,35,80,81]; Noether theory with time delay, see [46,77]; Noether theory for nonlinear dynamical systems, see [36,82]; as well as Noether theory for fractional systems of variable order, see [62,76]. Recently, Noether theory was extended to time scales, see for instance, [18,29,50,51,55,63,79,83].…”

Section: Introductionmentioning

confidence: 99%

Noether theory for Birkhoffian systems with nabla derivatives

Song¹,

Yi²

2017

J. Nonlinear Sci. Appl.

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There are discrete phenomena which happen only on discrete time or hold discrete space structures such as economy series, population dynamics et al.. Then there is a tool needed for these discrete issues or applications. Time scale is one of the useful tools to solve some discrete problems. In this paper, time scale is used to establish discrete Pfaff-Birkhoff principle and achieve discrete Birkhoff equations, discrete Noether identity and discrete conserved quantity for the discrete Birkhoffian system. Firstly, Birkhoff equations, Noether identity and Noether theorem with nabla derivatives on time scales are investigated by using the isochronous variational principle. Secondly, some special cases, especially the discrete Birkhoffian system are discussed. Thirdly, another method, i.e., the duality principle is introduced for the Birkhoffian system on time scales. And finally, an example is given to illustrate the results and methods.

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Section: Introductionmentioning

confidence: 99%

Noether theory for Birkhoffian systems with nabla derivatives

Song¹,

Yi²

2017

J. Nonlinear Sci. Appl.

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“…Since Noether unveiled the profound relations between symmetries and conservation laws, many researches on them were done [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Recently, symmetry theories have been extended to discrete mechanics and equations [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Perturbation to Symmetry and Adiabatic Invariants of General Discrete Holonomic Dynamical Systems

Wang

Zhu

2011

Acta Phys. Pol. A

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“…Fu et al discussed Noether symmetry, Lie symmetry, Mei symmetry, conformal invariance, and conserved quantities of continuous mechanico-electrical systems first [9][10][11]. Further, they investigated Noether symmetry and the conservation law of discrete mechanico-electrical systems [12,13]; based upon the property of the discrete models entirely inheriting the symmetry of the continuous systems, they presented Hojman conserved quantities and Lie symmetries of discrete mechanico-electrical coupling systems by Lie groups of transformations of continuous systems [14].…”

Section: Introductionmentioning

confidence: 99%

“…(10)-(12), neglecting the second-and higher-order terms of ε, and considering Eqs. (5)-(7), we can obtain the criterion of form invariance.Criterion For the discrete mechanico-electrical system (5)-(7), if the Lie group equations (8) of the infinitesimal transformations satisfy…”

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confidence: 99%