Symmetries of Lagrange system subjected to gyroscopic forces

Hui-Bin, Wu; Feng-Xiang, Mei

doi:10.7498/aps.54.2474

Cited by 5 publications

(4 citation statements)

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“…For Noether symmetry we can deduce the invariant. Theorem 1 For the Lagrange system (11), if the generators ξ 0 (t, 𝑞, q), ξ s (t, 𝑞, q) of the infinitesimal transformations have Noether symmetry (37), there exist fractional conserved quantities as…”

Section: Variable Order Fractional Noether Theorem Of Neuronal Membra...mentioning

confidence: 99%

“…In the proving process of this theorem we have used condition (37) and variable order fractional Lagrange equation (11).…”

Section: Variable Order Fractional Noether Theorem Of Neuronal Membra...mentioning

confidence: 99%

“…Since Noether revealed the relations between symmetry and conserved quantities in her eminent paper, [9] Noether theorem has had various extensions and has been applied in physics and mechanics. [10][11][12][13][14][15][16][17][18][19][20][21][22] Fractional calculus is increasingly important as it can more exactly describe complex phenomena in science and engineering. Fractional Noether theorem has been extended to the fractional Lagrange system, Hamilton system, generalized Hamilton system, Birkhoff system, and so on.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Variable Order Fractional Noether Theorem Of Neuronal Membra...mentioning

confidence: 99%

“…In the proving process of this theorem we have used condition (37) and variable order fractional Lagrange equation (11).…”

Section: Variable Order Fractional Noether Theorem Of Neuronal Membra...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…(17) It is easy to verify that they satisfy Eqs. (10), so the infinitesimal generators (17) are Mei symmetrical for the system (16).…”

Section: Illustrative Examplesmentioning

confidence: 99%

A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems

Ding¹,

Fang²,

Wang³

et al. 2007

Commun. Theor. Phys.

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A new type of conserved quantity, which is induced from the Mei symmetry of Lagrange systems, is studied.The conditions for that the new type of conserved quantity exists and the form of the new type of conserved quantity are obtained. An illustrated example is given. The Noether conserved quantity induced from the Mei symmetry of Lagrange systems is a special case of the new type of conserved quantity given in this paper.

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