A new Lagrangian density for all four Maxwell’s equations

Zheng, Chengbo; Wang, Zuojun

doi:10.1016/j.ijengsci.2010.08.002

Cited by 2 publications

(5 citation statements)

References 2 publications

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“…) and(22) are in fact one and the same thing derived from the circuit equation of the helix resonator, as that indicated by the constraint equation(20). This fact leads to an equality w…”

mentioning

confidence: 83%

“…In this paper, we introduce the Lagrangian density [21][22][23] and dissipation function [24] density for the Lagrangian description of the electrodynamics in two kinds of typical dispersive and absorptive metamaterials. The first metamterial we considered is the 'double-negative metamaterial' composed of wires [25] and splitrings [26] array, which can have negative refractive index in some frequency range when both the permittivity and permeability are negative [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

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Lagrangian dynamics approach for the derivation of the energy densities of electromagnetic fields in some typical metamaterials with dispersion and loss

Luan

2018

J. Phys. Commun.

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The Lagrangians and dissipation functions are proposed for use in the electrodynamics of the doublenegative and chiral metamaterials with finite loss. The double-negative metamaterial considered here is the 'wires and split-rings' periodic structure, while the chiral metamaterial is the 'single-resonance helical resonators' array. For either system, application of Legendre transformation leads to a Hamiltonian density identical to the energy density obtained in our previous work based on the Poynting theorem and the mechanism of the power loss. This coincidence implies the correctness of the energy density formulas we obtained before. The Lagrangian description and Hamiltonian formulation can be further developed for exploring the properties of the elementary excitations or quasiparticles in dispersive metamaterials due to light-matter interactions.

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“…) and(22) are in fact one and the same thing derived from the circuit equation of the helix resonator, as that indicated by the constraint equation(20). This fact leads to an equality w…”

mentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Lagrangian dynamics approach for the derivation of the energy densities of electromagnetic fields in some typical metamaterials with dispersion and loss

Luan

2018

J. Phys. Commun.

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“…The Lagrangian density L d corresponds to that proposed by Zheng and Wang [18] if both current and density of a monopole is assumed zero.…”

Section: From Electromagnetism To Circuit Theory Letmentioning

confidence: 99%

“…The Rayleigh's dissipation function D is defined by (17). And then, the movement of the system, namely the behavior of the circuit, is known to be determined by the Euler-Lagrange equation (18).…”

Section: Cumulated Electric Chargementioning

confidence: 99%

“…where R s is the resistance of a resistor s, dot on a variable is its time derivative, and x is any independent variable contained in either L or D. As shown later, the variable x is any one of the fluxes φ, cumulated electric charges q, or Lagrangian multipliers λ that are independent in the system. Equations (16)- (18) are the basic structure of the circuit theory on Lagrangian dynamics. In order to perform an analysis on a real system, we should determine L .…”

Section: Cumulated Electric Chargementioning

confidence: 99%

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A generalized method for Lagrangian modeling of power conversion circuit with integrated magnetic components

Umetani

2012

IEEJ Transactions Elec Engng

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A generalized Lagrangian is proposed to enable systematic analysis of integrated magnetic components. Although a few conventional theories are known that handle magnetic circuit, they cause difficulties in modeling or analysis, especially when applied to a highly integrated core. These difficulties are avoided in the proposed theory, as its Lagrangian is configurable directly from the physical core structure. As an example, the Lagrangian of the trans-linked three-phase boost converter is presented. Along with the Lagrangian, two types of circuit analysis are also presented: one is to obtain the state-space model of the converter; the other is to translate the integrated magnetic component into an equivalent circuit of basic components such as transformers and inductors. The analyses show the usefulness of the proposed method in practical applications.

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A new Lagrangian density for all four Maxwell’s equations

Cited by 2 publications

References 2 publications

Lagrangian dynamics approach for the derivation of the energy densities of electromagnetic fields in some typical metamaterials with dispersion and loss

Lagrangian dynamics approach for the derivation of the energy densities of electromagnetic fields in some typical metamaterials with dispersion and loss

A generalized method for Lagrangian modeling of power conversion circuit with integrated magnetic components

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