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“1.像几何学一样,理性力学必须建立在显然正确的公理上;2.力学的进一步事实由数学证明给出。”1743年达朗贝尔的这两句话点出了理性力学的核心。 牛顿的“自然哲学”(1687)是理性力学的第一部著作。在前人探索的基础上,他总结出力学运动三定律。从这些简单的公理出发,物体(质点)力学运动的全部主要性质便由演绎得出。 理性力学的另一个先驱者J·伯努利从事变形体力学的研究。他用四种方法推导出沿长度受任意载荷的弦的平衡方程(1691—1704)。通过实验他发现,伸长和张力并不满足胡克所提示的线性关系;他一直认为线性关系不能作为物性的一般原理。他首先得到杆的弯曲理论,当杆为直线时,就变成“elastica”的微分方程(1694)。 1788年拉格朗日发展了分析力学,其中许多内容是符合达朗贝尔的框架的。
1. Like geometry, rational mechanics must be based on manifestly correct axioms; 2. Further facts of mechanics are given by mathematical proofs. “These two words from 1743, by Dalambel, point to the core of rational mechanics. Newton’s Philosophy of Nature (1687) is the first book of rational mechanics. On the basis of his predecessors’ exploration, he summed up the three laws of mechanics. Starting from these simple axioms, all the main properties of the mechanics of objects (particles) are deduced. J Bernoulli, another pioneer of rational mechanics, is engaged in the study of deformation mechanics. He uses four methods to derive the equilibrium equations (1691-1704) for strings subjected to arbitrary loads along their length. Through experiments, he found that elongation and tension did not satisfy the linear relationship suggested by Hook; he always thought that the linear relationship can not be used as a general principle of physical properties. He first got the bending theory of the rod, and when the rod is a straight line, it becomes the differential equation of ”elastica" (1694). 1788 Lagrange developed analytical mechanics, many of which are in line with Datacraft’s framework.