通过分析相应特征方程根的性质，给出系统稳定的一个充分条件。
By studying the properties of roots for the corresponding characteristic equation, the sufficient conditions under which the equation is stable are given.
本文利用特征方程根的性质，研究了开口圆柱薄壳精确微分方程的特征方程的渐近解。
Using the root of the characteristic equation, this paper studies the asymptotic solution of the characteristic equation of the open circular cylindrical thin shells.
首先，通过对系统线性化方程的特征方程根的分布分析，给出了滞量对系统稳定性影响的具体结论和公式。
First locally linearizing nonlinear system at equilibrium to investigate show stability of system, obtain some practicability conclusions and formulas.
特征方程的根决定了系统的稳定性以及对各种输入的响应特性。
The roots of the characteristic equation determine the stability of the system and the general nature of the transient response to any input.
文中也提出了利用分划曲线来判定系统特征方程具有全部负实部根的方法。
Methods of using the D-decomposition curves to judge whether all the roots of the characteristic equation possess a negative real part are also discussed.
利用根轨迹法，分析了特征方程。
Using the root locus method, the characteristic equations are analyzed.
众所周知，时滞系统的特征方程对某一固定的时滞来说有无穷多个根，并且这些根也是很难解出的。
As everyone knows that the characteristic equations of the delay systems have infinite roots for a fixed delay and it is hard to solve for them.
该文还阐明了对二阶对称张量成立的关于特征方程的重根与重向的一些结论对非对称二阶张量不一定成立。
The paper illustrates the conclusions about the multiple root of characteristic equation and characteristic vector which fit symmetric tensor of rank two may unfit unsymmetric tensor.
对特征方程利用根与系数的关系，导出了一个计算基频的简便公式，并结合实例说明其有一定的实用价值。
A simple formula for finding basic frequency is derived by use of relation of root and coefficient, and an example is enumerated to illustrate its application.
根据总体稳定性判据，闭环系统稳定，当且仅当所有的特征方程的根有负面真正的部分。
According to the General Stability Criterion, a closed loop system will be stable if and only if all the roots of the characterized equation have negative real parts.
该一维有限元列式只需对扇形区域在角度方向上离散，最后的总体方程为一个二次特征根方程。
Discretization in angular coordinate is needed only and the global equation is a second order characteristic matrix equation.
特征方程之根？称为本征值或特征值。
The roots? Of the characteristic equations are known as eigenvalues, or characteristic values.
进一步，即使可以精确地得到特征方程，我们依然无法在有限精度的限制下去计算方程的根。
Furthermore, even if the exact characteristic equation can be obtained, we could not compute the roots of the equation in the demanding precision.
本文从无阻尼系统出发，理论上分析了转子系统振动方程的特征根，特征向量所具有的特点。
In this paper, the properties of eigenvalues and eigenvectors of rotor systems are discussed. The derivation shows that eigenvalues are imaginary in non-damping systems, and eigenspaces are complete.
利用常数变易法求解具有实特征根的四阶常系数非齐次线性微分方程，在无需求其特解及基本解组的情况下给出其通解公式，并举例验证公式的适用性。
Demonstrated in this paper is how the Constant-transform method, the typical method for solving differential equations of order one, is used in solving linear differential equations of order three.
摄动理论显示，对于特征方程系数的小幅度扰动即可导致根的大幅度变化。
Perturbation theory indicates that small perturbation of the coefficients could lead to the big perturbation of the root.
考虑阻尼力后，结构的特征方程应有复数根，因而通常用于求解多项式方程实数根的二分法不再适用。
The consideration of damping force leads to a fact that there exist complex roots to the characteristic equation for the structures.
本文指出了弱粘弹性材料结构的特征值是一组有理分式多项式方程的根，并给出了关于这些有理分式多项式方程根的一个定理。
It is pointed out that the eigenvalues of these structures are the roots of a series of rational fraction polynomial equations. A theorem about the roots of these equations is proved in the paper.
采用降阶和特征根 （欧拉 ）方法 ，给出了一类三维二阶常系数微分方程组的通解公式 ，并通过算例与拉氏变换法进行了比较。
With the variable replacement method, general solution formulae were given to the linear differential systems with complex constant coefficients and that with a class of complex variable coefficients.
给出一种简便的二次曲面简化方程的基本定理，特别给出二重零特征根二次曲面简化方程的定理。
This paper presents a basic law of the simplified equation of surface of degree 2, especially the law of the simplified equation of surface of degree 2 with two equal zero roots.
研究了三阶Poincaré差分方程解的渐近性质。这种差分方程对应的常系数线性差分方程的特征方程有重根。
We studied the asymptotic behavior of solutions to third order Poincaré difference equation whose characteristic equation has multiple roots.
研究了三阶Poincaré差分方程解的渐近性质。这种差分方程对应的常系数线性差分方程的特征方程有重根。
We studied the asymptotic behavior of solutions to third order Poincaré difference equation whose characteristic equation has multiple roots.
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