二自由度自治Lagrange系统的奇点稳定性

The stability of singular points of two degree of freedom autonomous Lagrange system

研究二自由度自治Lagrange系统的奇点稳定性.首先,给出二自由度自治Lagrange系统的微分方程;其次,得到该系统的奇点方程并将Lyapunov间接法推广到该系统;最后,得到判断该系统奇点稳定性的定理并举例说明结果的应用.

The stability of singular points of two degree of freedom autonomous Lagrange system is studied. Firstly,the differential equations of two degree of freedom autonomous Lagrange system are given; then,the singular points equations of this system are obtained and the Lyapunov indirect method is extended to the system; finally,the method of judging the stability of singular points of this system is obtained and an example is given to illustrate the application of the results.