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Euler-Lagrange equations and Noether’s theorem of multi-scale mechano-electrophysiological coupling model of neuron membrane dynamics

Wang Peng

Journal of Theoretical and Applied Mechanics

2023

Vol. 61 nr 4

847--856

Noether’s theorem is applied into a multi-scale mechno-electrophysiological coupling model of neuron membrane dynamics. The Euler-Lagrange equations in generalized coordinates of this model are deduced by the nonconservative Hamilton principle. The Noether symmetry criterion and conserved quantities based on the Lie point transformation group are given. The influence of external non-potential forces and material parameters on the forms of Noether conserved quantities is detailed discussed, which indicates that the conserved quantities are very depending on the loading rate and mechanical parameters of the membrane.

Lie symmetries and conserved quantities of discrete constrained Hamilton systems

Mingliang Z.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 3

61--70

In this paper, the Lie symmetry theory of discrete singular systems is studied in phase space. Firstly, the discrete canonical equations and the energy evolution equations of the constrained Hamilton systems are established based on the discrete difference variational principle. Secondly, the Lie point transformation of discrete group is applied to the difference equations and constraint restriction, and the Lie symmetry determination equations of the discrete constrained Hamilton systems are obtained; Meanwhile, the Lie symmetries of singular systems lead to the discrete Noehter type conserved quantities when the structure condition equations (discrete Noether identity) are established. Finally,an example is given to illustrate the application, the results show that the conservative constrained Hamilton systems also have the discrete energy conservation.