Birkhoff系统约化的Routh方法

Routh method of reduction of Birkhoffian systems

研究Birkhoff系统的约化.首先,列出系统的运动微分方程及其循环积分;其次,构造Birkhoff系统的Routh函数组,利用循环积分约化Birkhoff系统的运动微分方程,并使约化后的动力学方程仍保持Birkhoff方程的形式;最后,举例说明结果的应用.

Reduction of Birkhoffian systems is studied. First, the differential equations of motion for the Birkhoffian systems are established and their cyclic integrals are given. Second, the Routh functions of Birkhoffian systems are constructed, and the order of the systems is reduced by using the cyclic integrals and the Birkhoffian form made to hold. Finally, an example is given to illustrate the application of the results.