Article ID: CBB001553278

Gearing up for Lagrangian Dynamics: The Flywheel Analogy in Maxwell's 1865 Paper on Electrodynamics (2015)


James Clerk Maxwell's 1865 paper, “A Dynamical Theory of the Electromagnetic Field,” is usually remembered as replacing the mechanical model that underpins his 1862 publication with abstract mathematics. Up to this point historians have considered Maxwell's usage of Lagrangian dynamics as the sole important feature that guides Maxwell's analysis of electromagnetic phenomena in his 1865 publication. This paper offers an account of the often ignored mechanical analogy that Maxwell used to guide him and his readers in the construction of his new electromagnetic equations. The mechanical system consists of a weighted flywheel geared into two independently driven crank wheels in what amounts to a mechanical differential. I will demonstrate how Maxwell made use of the analogy between his flywheel system and electromagnetic induction to ground his study of electromagnetism in clear mechanical conceptions and to structure the derivation of the equations that together are now recognized as Maxwell's equations for electrodynamics. By reconceiving specific components of his model in electromagnetic terms, while at the same time retaining many of the relations between concepts in the mechanical case, Maxwell gradually assembled increasingly generalized equations for electromotive force. Maxwell thus realized a much sought after balance between physical analogy and abstract mathematics in this, the last of his three seminal papers on electromagnetism.

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Authors & Contributors
Lambert, Kevin Thomas
McCartney, Mark
Tazzioli, Rossana
Cat, Jordi
Hyder, David Jalal
Hong, Sungook
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Historia Mathematica
Science in Context
Physics in Perspective
Journal of the History of Ideas
European Physical Journal H
Oxford University Press
Cambridge University Press
University of California, Los Angeles
University of Minnesota
Pavia University Press
Metaphors; analogies
Mathematics and its relationship to science
Maxwell, James Clerk
Lodge, Oliver
Faraday, Michael
Helmholtz, Hermann Ludwig Ferdinand von
Grassmann, Hermann Günther
Kelvin, William Thomson, Baron
Time Periods
19th century
20th century
Great Britain
Pisa (Italy)

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