Dependence of Equilibrium Stability of First Order Lagrange Systems on Parameters
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摘要: 带附加项的定常一阶Lagrange系统在一定条件下可化成梯度系统,利用梯度系统的特性研究了带附加项的一阶Lagrange系统的稳定性及其对参数的依赖关系.以具体实例在参数平面上划出稳定性区域,进一步说明了参数的变化不仅可改变稳定性质,而且可改变平衡点的参数.
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关键词:
- 一阶Lagrange系统 /
- 梯度系统 /
- 稳定性 /
- 参数
Abstract: Steady first order Lagrange systems with additive terms were considered as gradient systems under certain conditions. The characteristics of the gradient system were used to study the equilibrium stability and its dependence on the parameters of the system. With two examples, the first order Lagrange systems’ stability domains were given in the parameter plane. Further, the analytical results indicate that change of the parameters not only influence the systems’ stability, but also influence the quantity of the equilibrium points.-
Key words:
- first order Lagrange system /
- gradient system /
- stability /
- parameter
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