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Article ID: CBB773667166

Deducing Newton’s second law from relativity principles: A forgotten history (2020)

Darrigol, Olivier (Author)

Archive for History of Exact Sciences
Volume: 74
Issue: 1
Pages: 1-43
Publication date: 2020
Language: English

URI: https://doi.org/10.1007/s00407-019-00230-2

DOI: 10.1007/s00407-019-00230-2

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Physics Motion (physical) Relativity Thermodynamics Mechanics 19th century France Newton, Isaac

In French mechanical treatises of the nineteenth century, Newton’s second law of motion was frequently derived from a relativity principle. The origin of this trend is found in ingenious arguments by Huygens and Laplace, with intermediate contributions by Euler and d’Alembert. The derivations initially relied on Galilean relativity and impulsive forces. After Bélanger’s Cours de mécanique of 1847, they employed continuous forces and a stronger relativity with respect to any commonly impressed motion. The name “principle of relative motions” and the very idea of using this principle as a constructive tool were born in this context. The consequences of Poincaré’s and Einstein’s awareness of this approach are analyzed. Lastly, the legitimacy and significance of a relativity-based derivation of Newton’s second law are briefly discussed in a more philosophical vein.

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