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James Clerk Maxwell[aut]Maxwell, James Clerk advancedIEMN Electromagnetic theoryItaly, whileLille University also mathematically enlarging Michael Faraday’s[aut]Faraday, Michael works. He declined NewtonianNewtonian mechanics for the formulation of new conceptual frameworks because more adequate for describing a field of new phenomenaPhenomena such as electromagnetism; so he also went beyondBeyond the Newtonian paradigmParadigm introducing a novelty in the relationship physics–mathematics based on new magnitudes, e.g., electric charge and energy instead of mass and force. However, through exactly which terms were these advances made? In particular, in A Treatise on ElectricityElectricity and MagnetismMagnetism, II, Part IV, Chapter IV–VII (1873) Maxwell aimed to formulate a dynamical justification for field equations; he focused on the fact that magnetic field appeared a complete kineticKinetic energy systemSystem. In this paper, we analyse and describe both: (a) what he called, Lagrange’s method of reducing the ordinary dynamical equations in Mécanique analytique (1788)––including––three methods used by Maxwell for expressing the kineticKinetic energy––detecting the existence of the terms of the form Tme, and (b) the application of the Lagrangian formulating through the equations of motion of a connected system.

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Lagrange’s Method and Lagrangian’s Mechanism in Maxwell’s A Treatise on Electricity and Magnetism (1873)

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  • 发表日期：

    2025年

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  • Raffaele Pisano,
  • Donatella Marmottini,
  • Andrea Durlo

摘要

James Clerk Maxwell[aut]Maxwell, James Clerk advancedIEMN Electromagnetic theoryItaly, whileLille University also mathematically enlarging Michael Faraday’s[aut]Faraday, Michael works. He declined NewtonianNewtonian mechanics for the formulation of new conceptual frameworks because more adequate for describing a field of new phenomenaPhenomena such as electromagnetism; so he also went beyondBeyond the Newtonian paradigmParadigm introducing a novelty in the relationship physics–mathematics based on new magnitudes, e.g., electric charge and energy instead of mass and force. However, through exactly which terms were these advances made? In particular, in A Treatise on ElectricityElectricity and MagnetismMagnetism, II, Part IV, Chapter IV–VII (1873) Maxwell aimed to formulate a dynamical justification for field equations; he focused on the fact that magnetic field appeared a complete kineticKinetic energy systemSystem. In this paper, we analyse and describe both: (a) what he called, Lagrange’s method of reducing the ordinary dynamical equations in Mécanique analytique (1788)––including––three methods used by Maxwell for expressing the kineticKinetic energy––detecting the existence of the terms of the form Tme, and (b) the application of the Lagrangian formulating through the equations of motion of a connected system.