Destabilization paradox
Destabilization paradox
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不稳定悖论
DOI：
10.1134/1.1753620
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发表时间：
2004
期刊：
影响因子：
0.8
通讯作者：
Oleg N. Kirillov
中科院分区：
文献类型：
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作者：
Oleg N. Kirillov
对于由式(1)描述的一般线性非保守系统，我们找到了函数qcr (k)的显式逼近，从而可以确定临界负荷的跳变和渐近稳定区域。此外，还得到了在弱耗散力和陀螺力的扰动下，特征值的轨迹及其分解成独立曲线的显式渐近表达式。我们考虑在由方程(1)描述的系统的参数k1， k2，…，kn-1和q构成的n维空间中点p0=（0，…，0,q0）。假设±1 ω0（其中ω0> 0）是长度为2的约当链算子A (q0)+ λ2M的双特征值，其余的±1 ω0， s（其中ω0， s> 0和s= 1,2，…，m-2）是虚数和sim-
In this work, for the general linear nonconservative system described by Eq.(1), an explicit approximation is found for the function qcr (k), which makes it possible to determine both the jump of the critical load and the asymptotic-stability region. In addition, explicit asymptotic expressions are obtained for the description of the trajectories of eigenvalues and their decomposition into independent curves under perturbations of the circulatory system by weak dissipative and gyroscopic forces.2. Let us consider the point p0=(0,…, 0, q0) in the n-dimensional space of the parameters k1, k2,…, kn–1, and q of the system described by Eq.(1). It is assumed that±iω0, where ω0> 0, are the double eigenvalues of the operator A (q0)+ λ2M with the Jordan chain of a length of 2 and the remaining eigenvalues±iω0, s, where ω0, s> 0 and s= 1, 2,…, m–2, are imaginary and sim-