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 引用本文: 陈菊, 郭永新, 刘世兴, 梅凤翔. Birkhoff 系统稳定性的动力学控制[J]. 力学学报, 2020, 52(4): 928-931.
Chen Ju, Guo Yongxin, Liu Shixing, Mei Fengxiang. DYNAMICAL CONTROL OF STABILITY FOR BIRKHOFFIAN SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 928-931.
 Citation: Chen Ju, Guo Yongxin, Liu Shixing, Mei Fengxiang. DYNAMICAL CONTROL OF STABILITY FOR BIRKHOFFIAN SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 928-931.

## DYNAMICAL CONTROL OF STABILITY FOR BIRKHOFFIAN SYSTEM

• 摘要: 本文研究 Birkhoff 系统和广义 Birkhoff 系统平衡稳定性的动力学控制. 首先建立系统的运动方程和平衡方程. 其次,研究 Birkhoff 系统中控制参数出现在 Birkhoff 函数中平衡稳 定性的动力学控制. 方法是通过选取控制参数使得 Birkhoff 函数 B 成为定号函数,而其时间导数 \dot B 为与 B 反号的常号函数. 再次,研究广义 Birkhoff 系统平衡稳定性的动力学控制,通过选取 Birkhoff 函数或附加项中包含控制参数的方法,使得 Birkhoff 函数是定号函数,而其时间导数为反号的常号函数,从而控制系统的平衡稳定性. 最后举例说明结果的应用.

Abstract: A dynamical control of the stability of equilibrium for the Birkhoffian system and generalized Birkhoffian system are studied. First, the equilibrium of motion and the equations of equilibrium of the systems are established. Secondly, the dynamical control of the stability of equilibrium for the Birkhoffian system where the Birkhoffian contain control parameters is investigated. The control parameters are chosen such that the Birkhoffian B becomes a definite function and its derivative of time \dot B is opposite sign. Thirdly, the dynamical control of the stability of equilibrium for Birkhoffian system where control parameters are contained in the Birkhoffian or in the additional terms is explored. Finally, some examples are given to illustrate the application of the results.

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