高维力学系统的能量方程  

Energy equations of high-order mechanical systems

作　　者：韩广才 刘志强 

机构地区：[1]哈尔滨工程大学航天与建筑工程学院,黑龙江哈尔滨150001 [2]哈尔滨工程大学机电工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2009年第11期1224-1227,共4页Journal of Harbin Engineering University

基　　金：黑龙江省自然科学基金资助项目(A2004-07)

摘　　要：在低维系统中,能量方程因其明晰的物理意义而得到广泛的应用,而研究高维力学系统的能量方程也同样具有理论价值和实际意义,如位移对时间的导数是速度,速度对时间的导数是加速度,这些具有明显的物理意义,而加速度的导数其物理意义就不是很清晰了,但具有理论上的意义.本文应用广义经典力学中关于广义拉格朗日函数、广义动量和广义哈密顿函数等概念,推导了高维系统的能量方程,文中举了实例具体说明新方程的应用,为力学数学系统能量方程的推广提供了一种途经.Energy equations are widely used in low-order mechanical systems and have clear physical meanings. On the other hand, energy equations for high-order mechanical systems may lack clear meaning, but still have theoretical and practical significance. It is clear that the derivation of displacement with respect to time is velocity and the derivation of velocity with respect to time is acceleration. However, the derivation of acceleration with respect to time has no obvious physical meaning, yet it has theoretical significance. Energy equations of high-order mechanical systems were derived in this paper using the generalized Lagrange functions, generalized momentum, and the Hamilton function in generalized classical mechanics. An example was given to show the application of the new energy equations. The research in this paper provides a new way to extend the application of energy equations in mathematics and mechanical systems.

关 键 词：广义经典力学 拉格朗日函数 正则方程 能量方程 

分 类 号：O414.1[理学—理论物理] O316[理学—物理]