Deducing Newton's second law from relativity principles: A forgotten history

摘要

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 Belanger's Cours de mecanique 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 Poincare'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.