牛頓以後力概念的發展與應用

Abstract

牛頓用他的運動定律與外力概念成功的解決了天體問題，將月球繞地球和地表蘋果落下用同一個原因解釋，提出了萬有引力的概念。 為了解決萬有引力和機械論的矛盾之處，許多科學家與哲學家都提出了各自的看法。最後，他們拋棄哲學觀點，將力視為是數學關係，用以解釋現象。 在應用上，Euler提出了新的分析方法：「將物質分割為質點，分析個別的運動狀態，最後利用連續性找出整體的運動模式」，並且使用代數方程式來表達，和Bernoulli、d’Alembert等人使用F=ma的方程式處理許多工程問題。 Lagrange則由牛頓力學為基礎發展出一套全新的動力學原理，透過使用虛速度原理的形式以及Clairaut將力寫成全微分的形式的方法，最後得到「Lagrange方程式」和「力學能守恆」，將物理學推至更高的境界，漸漸發展成今日的樣貌。

Using the laws of motion and concept of force, Newton had a great success on sovling the astronomical problems. Coming up with the concept of universal gravitation, he can explain both the motion of the moon which surround the earth and the fall of apple by the same reason. Many scientists and philosophers put their opinion forward to resolve the contradiction of the universal gravitation and the mechanism. Eventually, they abandoned the philosophical perspective and regard force as mathematical ralation by which can gives explaination to natural phenomenon. Euler proposed a new method:”Divide the body into mass points, analyze each states of motion, and find the overall pattern of motion by continuity. He expressed it in terms of algebraic equations and dealt with many engineering problems by the equation “F=ma” with Bernoulli, d’Alembert, and so on. On the other hand, by using the form of virtual velocity and the method of Clairaut, who wrote force as total derivative, Lagrange developed brand new dynamic principles based on Newtonian mechanics, and dirived “Lagrange equations” and “conservation of mechanical energy” eventually. His work brought the research of physics to higher level, forming the appearance of nowadays gradually.