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中文摘要：
利用Noether理论对约束广义Birkhoff系统的稳定性问题进行了研究,给出了约束广义Birkhoff系统的受扰运动方程;得到了约束广义Birkhoff系统的1次近似方程,利用Lyapnnov 1次近似理论,建立了约束广义Birkhoff系统稳定性的判据;利用Noether守恒量构造Lyapnnov函数,建立了直接法的系统平衡状态稳定性的判据,并举例说明它的应用.
英文摘要：
The problem on the stability of motion for a generalized Birkhoffian system with constrains are studied by the Noether theong.The disturbed equations of motion and their first approximation for the system are established.The criterion of stability of motion for the system was set up by using Lyapnnov’ s first approximation theory.The Lyapnnov’s function was constructed by the Noether conserved quantity and the criterion of stability of motion for the system was also set up by using Lyapnnov’s direct method.Finally,the example is given to illustrate the application of the results.
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