牛顿力学与分析力学对动力学问题的解法比较  

Comparison of Newtonian mechanics and analytical mechanics in solving the dynamics problem

作　　者：吕嫣[1] 崔崧[1] 李慧玲[1] LüYan;CUI Song;LI Huiling(College of Physical Science and Technology,Shenyang Normal University,Shenyang 110034)

机构地区：[1]沈阳师范大学物理科学与技术学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2020年第5期451-454,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11703018)。

摘　　要：力学体系的动力学问题可以由不同方法进行求解。理论力学包含牛顿力学和分析力学两大体系,从方法上就包含了两种解题方法。引入一动力学例题,分别用牛顿力学方法和分析力学方法对其求解,后者又分别应用了拉格朗日方程、哈密顿正则方程及哈密顿原理求出体系的力学规律。不同的方法求出的结果完全相同,但两种方法的解题思想是不同的。牛顿力学方法依据牛顿运动定律,通过建立运动微分方程求解问题。分析力学方法则是以一些基本原理及相应的动力学方程为基础,通过数学分析的方法求解问题。对于多约束问题分析力学方法显示出优越性,但物理意义不明显。The dynamics problem of a mechanics system can be solved by different methods.Theoretical mechanics consists of two systems:Newtonian mechanics and analytical mechanics.So there are two methods to solve the problem.For a dynamics problem,the Newtonian mechanics method and the analytical mechanics method are used to solve the problem respectively.Lagrange equation,Hamilton canonical equations and Hamilton's principle are used to solve the problem in the analytical mechanics method.The results of the different methods are exactly the same.However the thoughts of the two methods are different.Newtonian mechanics is based on Newton's law of motion,it solves unknown quantities by constructing differential equations of motion.Analytical mechanics is based on some general principles and their dynamics equations,it applies mathematical analysis to solve the problem.For the multi-constrained problem,the analytical mechanics method shows its superiority,but the physical meaning is not obvious.

关 键 词：理论力学 牛顿力学 分析力学 力学体系 广义坐标 拉格朗日方程 哈密顿正则方程 哈密顿原理 

分 类 号：O411[理学—理论物理]