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完整系统三阶Lagrange方程的一种推导与讨论
引用本文:马善钧,徐学翔,黄沛天,胡利云.完整系统三阶Lagrange方程的一种推导与讨论[J].物理学报,2004,53(11):3648-3651.
作者姓名:马善钧  徐学翔  黄沛天  胡利云
作者单位:江西师范大学物理与通信电子学院,南昌 330027
基金项目:国家自然科学基金(批准号:19972010)资助的课题.
摘    要:从牛顿运动方程出发,推导了完整系统关于广义加速度的Lagrange方程.讨论了该方程与传统分析力学中的Lagrange方程的相容性问题.结果显示,三阶Lagrange方程可以通过对Lagrange方程求一阶时间导数得到,表明它们是相容的.因此三阶Lagrange方程提供了一种不同于传统Lagrange方程方法的求解物体运动方程的途径. 关键词: Lagrange方程 加速度能量 广义坐标

关 键 词:Lagrange方程  加速度能量  广义坐标
收稿时间:2004-02-13
修稿时间:3/8/2004 12:00:00 AM

The discussion on Lagrange equation containing third order derivatives
Ma Shan-Jun,Xu Xue-Xiang,Huang Pei-Tian and Hu Li-Yun.The discussion on Lagrange equation containing third order derivatives[J].Acta Physica Sinica,2004,53(11):3648-3651.
Authors:Ma Shan-Jun  Xu Xue-Xiang  Huang Pei-Tian and Hu Li-Yun
Abstract:In this paper, the third order Lagrange equation is obtained, by which can be obtained motion equation of a body. This equation contains third order rate of change of generalized coordinates and the rate of change of force. In addition, the third order Lagrange equation and the fraditional Lagrange equation are used to solve the same problem of the motion of a body, and their results are discussed. Finally, it is pointed out that the third order Lagrange equation provides a method of obtaining equation of motion which is different from that of the traditional Lagrange equation.
Keywords:Lagrange equation  energy of acceleration  generalized coordinates
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