Maxwell-Bloch top系统的Poisson几何与稳定性问题
Poisson geometry of the Maxwell-Bloch top system and stability problem
摘要：
在Poisson几何的框架下，研究了Maxwell-Bloch陀螺系统的动力学，其中包括Maxwell-Bloch和Lorenz-哈密顿方程作为特例.给出了运动常数以及解与摆解的关系。确定了平衡态，并对其进行了完整的稳定性分析。结果被应用到最优控制问题的李群G4。
英文摘要：
Dynamics of Maxwell-Bloch top system, that includes Maxwell-Bloch and Lorenz-Hamilton equations as particular cases, is studied in the framework Poisson geometry. Constants of motion as well as the relation of solution to that of pendulum are presented. Equilibrium states are determined and their complete stability analysis are performed. Results are applied to an optimal control problem on the Lie group G4.
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