讲授力学原理统一性——以弹簧振子为例UNIFICATION OF FIVE MECHANICS PRINCIPLES BASED ON THE SPRING-MASS SYSTEM
刘建林
摘要(Abstract)：
对一个系统进行力学分析可以运用不同的力学原理而得到相同结果。本文以弹簧振子为例,详细阐述了牛顿第二定律、机械能守恒定理、拉格朗日方程、哈密顿正则方程、哈密顿变分原理这五种力学原理之间的相互关系。其中牛顿第二定律是从受力角度进行分析,而机械能守恒定理、拉格朗日方程、哈密顿正则方程则是从能量角度出发。哈密顿变分原理则为更为普遍的力学原理,通过对其变分可以推导出拉格朗日方程、哈密顿正则方程以及运动微分方程。弄清楚这五种力学原理的统一性,有助于我们更加合理地选择运用它们去解决工程问题。
关键词(KeyWords)： 牛顿第二定律;机械能守恒定律;拉格朗日定理;哈密顿正则方程;哈密顿原理
基金项目(Foundation): 国家自然科学基金(11672335)资助
作者(Author): 刘建林
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