DERIVING NEWTON’S SECOND LAW FROM RELATIVITY PRINCIPLES

Abstract

Abstract After Huygens’s pioneering derivation of the laws of free fall from Galilean relativity, many authors used this relativity and Newton’s accelerative relativity to derive Newton’s second law of motion (the law of acceleration). In the eighteenth century, Euler and d’Alembert implicitly relied on Galilean relativity in their rational justifications of the laws of mechanical motion. Late in the century, Laplace derived the discrete-impulse version of Newton’s second law from Galilean relativity. Many French writers followed suit in nineteenth-century physics textbooks. A few of them used a principle of accelerative relativity, Bélanger’s “principle of relative motions,” to derive the continuous version of Newton’s second law. Poincaré criticized these derivations, retained Galilean relativity only, and amplified the idea of relativity as an organizing principle. He soon turned Bélanger’s name into “principle of relativity.”