广义Tzénoff函数的构造及求解完整系统守恒量的简单方法  

The simple method for constructing the generalized Tzénoff function and solving the holonomic system conserved quantities

作　　者：郑世旺[1] 王建波[1] 

机构地区：[1]商丘师范学院物理与电气信息学院,河南商丘476000

出　　处：《商丘师范学院学报》2014年第6期29-34,共6页Journal of Shangqiu Normal University

基　　金：国家自然科学基金资助项目(11372169)

摘　　要：利用Tzénoff方程研究动力学性质必须首先知道系统的Tzénoff函数,但构造一个实际力学系统的Tzénoff函数是比较困难的.本文结合实际力学系统给出了构造广义Tzénoff函数的方法,研究了在完整约束条件下的广义Tzénoff方程,发现利用广义Tzénoff方程这种高阶微分方程可直接得到广义加速度,最后给出了广义Tzénoff方程Lie对称性的定义,得到了求解守恒量的简单方法.To research the kinetic properties by using the Tzenoff equations, the system Tzenoff function must be gotten firstly. But it is difficult to construct the Tzenoff function of an actual kinetic system. So in this paper, we give a method of constructing generalized Tzenoff function by combining the actual kinetic system and find that the generalized acceleration can be obtained directly by using the such higher - order generalized Tzenoff function. At last, the definition of the Lie symmetry of the generalized Tzenoff function is provided and the simple method of solving the conserved quantities is obtained.

关 键 词：广义Tzénoff函数的构造 广义Tzénoff方程 完整系统 守恒量 

分 类 号：O320[理学—一般力学与力学基础]