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

Wang, P.; Zhu, Hengjiang

doi:10.12693/aphyspola.119.298

Cited by 3 publications

(3 citation statements)

References 35 publications

(37 reference statements)

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“…For brevity of notation, we consider a one--dimensional discrete dierence variational Hamil- (25) ton system. The Hamiltonian of the system is…”

Section: The Noether Symmetry and Discrete The Noether Exact Invariantmentioning

confidence: 99%

“…Recently, Zhang et al [24] presented the concept of discrete high-order adiabatic invariant, and studied the perturbation to the the Noether symmetry and the Noether adiabatic invariant of the general discrete holonomic system. Wang and Zhu [25] further discussed perturbation to symmetry and adiabatic invariants of general discrete holonomic dynamical systems on a uniform lattice. However, perturbation to symmetries and adiabatic invariants of the discrete Hamilton systems has never been studied so far.…”

Section: Introductionmentioning

confidence: 99%

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Perturbation to Noether Symmetry and Noether Adiabatic Invariants of Discrete Difference Variational Hamilton Systems

Zhang

Fang

2012

Acta Phys. Pol. A

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The perturbation to the Noether symmetry and the Noether adiabatic invariants of discrete dierence variational Hamilton systems are investigated. The discrete the Noether exact invariant induced directly by the the Noether symmetry of the system without perturbation is given. The concept of discrete high-order adiabatic invariant is presented, the criterion of the perturbation to the Noether symmetry is established, and the discrete the Noether adiabatic invariant induced directly by the perturbation to the Noether symmetry is obtained. Lastly, an example is discussed to illustrate the application of the results.

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“…For brevity of notation, we consider a one--dimensional discrete dierence variational Hamil- (25) ton system. The Hamiltonian of the system is…”

Section: The Noether Symmetry and Discrete The Noether Exact Invariantmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Perturbation to Noether Symmetry and Noether Adiabatic Invariants of Discrete Difference Variational Hamilton Systems

Zhang

Fang

2012

Acta Phys. Pol. A

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“…The well known Noether symmetry has broad applications in mathematics, dynamics, and physics [1][2][3][4][5][6][7], it always can lead to conserved quantities. In fact, it is also named variational symmetry [3].…”

Section: Introductionmentioning

confidence: 99%

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Wang

Feng

2017

Acta Phys. Pol. A

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Basing on the analytical mechanics methods, the Lagrangian equations of thin elastic rod is constructed. The definition of conformal invariance for the Lagrange mechanics of elastic rod is given. The criterions that conformal invariance of elastic rod is the Lie symmetry are obtained based on the Lie point transformation group. The structure equation and conserved quantity deduced from conformal invariance of elastic rod are constructed. Take twist rod as an example to illustrate the application of the results got in this paper.

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Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

Wang

2023

Chinese Phys. B

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Noether theorem is applied into a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics. The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics, is given. The variable orders fractional Noether symmetry criterion and Noether conserved quantities are given. The forms of variable orders fractional Noether conserved quantities correspond to Noether symmetry generators solutions of the model under different conditions are detailed discussed, and it is found that the expressions of variable orders fractional Noether conserved quantities are closely depending on the external nonconservative forces and material parameters of neuron.

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

Cited by 3 publications

References 35 publications

Perturbation to Noether Symmetry and Noether Adiabatic Invariants of Discrete Difference Variational Hamilton Systems

Perturbation to Noether Symmetry and Noether Adiabatic Invariants of Discrete Difference Variational Hamilton Systems

Conformal Invariance and Conserved Quantities for Lagrange Equation of Thin Elastic Rod

Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

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