牛顿关于向心力概念的数理思想

NEWTON'S THOUGHTS ON THE MEASURING OF CENTRAL FORCE

牛顿创立的“向心力”（viscentripeta）概念是牛顿力学思想中的基本概念。牛顿在不同历史阶段（1679／1680年间与胡克的通信、1684年《论运动》系列手稿、1687年《原理》第一版、17世纪90年代关于《原理》的修订）中所给出的与“向心力”有关的数学表达式分别是：（1）F∝C2／r3-d2r／dt2；（2）F∝C2／r2[1／r—d2（1／r）／d2；（3）F∝-d（v2）／dr；（4）F∝v2／psina。它们体现了牛顿数理思想的简单性原则。牛顿在1670年有关曲率半径的微分表达式、1685年表述的运动合成的平行四边形法则，是牛顿数理思想发展过程中的重要环节。

Of the five basic forms of measuring central force, which from point to point draws a body from straight into a curving orbit about the force-centre, four appear at different times in the growth to maturity of Newton's thought. The four different guises of what is fundamentally the same mathematical measure of the central force appear at, namely, in the Borellian notions in letters Newton sent to Hooke in late 1679, that were set out by him in his 'De Motu Corporum' of 1684 which passed to be Proposition 6 of Book 1 of his Principia, the generalised one which first appears in Proposition 41 following, and the curvature measure which first appears in Newton's revisions of the Principia in the early 1690's. In the past at tention has all but always been given to the primary one in the Principia, but all are well founded and can serve each as the basis for a general theory of motion under continuously deviating action of a central force. Generally spoken, Newton's calculus formula of curvature and the parallelogram of motion are the key steps in the development of Newton's mathematico-physical thoughts.