Historical Studies on the systematization of classical mechanics in the 18^<th> century

点击翻译按钮获取中文摘要

Classical mechanics is generally regarded as having been founded by Isaac Newton in the late 17th century, but his mathematical arguments in Principia are geometrical and very different from those of ours. In this study, we discuss the process of constructing the analytic and systematic system of classical mechanics in the 18th century, particularly the mechanical theory of Leonhard Euler who played the principal role in this process.Euler firstly used the systematic method of setting the coordinate axes fixed in space and deriving the equation of motion as the second-differential equation for each coordinate. From it, he also the conservation laws of "vis viva" (kinetic energy), linear momentum and angular momentum. Further he extended the object of his method from mass points to rigid bodies, and derived the so-called Euler equation of rigid bodies.This transition of mechanics to new one founded on the analytical calculus happed in the second part of 1740s by Euler's study of motion of planets and rigid bodies. It is very important that in this period the mathematical formula of Euler's equation of motion has changed largely.In his younger period, he derived the equation of motion from Galileo's law of free fall, and it had the particular formula of the first-order differential equation of space. Later, its formula has changed to the second-order differential equation of coordinate and the influence of Galileo's law has decreased, but we can distinguish its influence in the factor 2 of his equation of motion and his unit system of mechanics.