Stabilization and destabilization of a circulatory system by small velocity-dependent forces
Stabilization and destabilization of a circulatory system by small velocity-dependent forces
复制标题
小速度相关力对循环系统的稳定和不稳定
DOI：
10.1016/j.jsv.2004.05.020
复制
发表时间：
2005
影响因子：
4.7
通讯作者：
A. P. Seyranian
中科院分区：
文献类型：
--
作者：
Oleg N. Kirillov;A. P. Seyranian
考虑非保守位置力下的线性自主机械系统。研究了与广义速度成比例的小力对系统稳定性的影响。得到了耗散力和陀螺力矩阵使系统渐近稳定的充要条件。详细研究了具有两个自由度的系统。找到并绘制了描述稳定矩阵结构和矩阵元素空间中的稳定域的显式公式。作为一个机械例子，分析了齐格勒-赫尔曼-琼摆的稳定性问题。
A linear autonomous mechanical system under non-conservative positional forces is considered. The influence of small forces proportional to generalized velocities on the stability of the system is studied. Necessary and sufficient conditions are obtained for the matrix of dissipative and gyroscopic forces to make the system asymptotically stable. A system with two degrees of freedom is studied in detail. Explicit formulae describing the structure of the stabilizing matrix and the stabilization domain in the space of the matrix elements are found and plotted. As a mechanical example, a problem of stability of the Ziegler–Herrmann–Jong pendulum is analyzed.