浅谈二阶微分方程与Kepler三大定律

A Brief Discussion on Second-Order Differential Equations and Kepler’s Three Laws

摘要: 微积分的一个重要应用就是微分方程，在工科院校的高等数学的课程当中，对于二阶常微分方程会花非常大的力气在二阶常系数线性常微分方程的求解中，对于其余的二阶常微分方程尤其是非线性的常微分方程很少涉及。本文通过对Kepler三大行星运动定律的数学推导，来说明非线性常微分方程才是实际当中碰到的大多数，以及微积分作为人类历史上的一项伟大发现的重要意义。

Abstract: An important application of calculus is differential equations. In the advanced mathematics courses of engineering colleges, a lot of effort is spent on solving second-order linear differential equations with constant coefficients, while other second-order differential equations, especially nonlinear differential equations, are rarely involved. This paper uses the mathematical derivation of Kepler’s three laws of planetary motion to illustrate that nonlinear differential equations are the majority of ordinary differential equations encountered in practice, and the importance of calculus as a great discovery in human history.