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.
求解高次实系数代数方程的根，对于控制系统的分析和综合设计有着重要意义。
Solving the algebra equation with real-coefficients of nth degree is of great importance for analysis and synthesis of a control system.
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.
本文提出的这种方法，它的特点在于：我们不是用牛顿迭代法去直接逼近方程的根，而是用牛顿迭代法去逼近方程的二次因子。
The method presented in this paper is not to approximate directly with Newton iterate the roots of a polynomial but to approximate its second order factors.
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.
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.
本文介绍了一种求实系数高次代数方程全部根的新方法。
This paper presents a new method in which all roots of a higher degree algebraic equation with real coefficients can be found out.
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.
不动点迭代方法是求解非线性方程近似根的一个重要方法，其应用非常广泛。
Fixed-Point Iteration method is an important technique to solve nonlinear equations for calculating approximate roots and applied widely.
本文提出一种通过对数复变换求非线性方程实数根数值解的方法。
A method to find real numerical solution of the nonlinear equation by logarithm complex conversion is presented in this paper.
提出了一个新的迭代公式，用此公式求解非线性方程根收敛速度快，且绝对收敛。
This paper presents a new iterative formula by which the solution of nonlinear equation had rapid and absolute convergence.
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.
基于高斯摄动方程，推导了卫星在同时考虑J2和大气摄动情况下的轨道根数变化方程。
The variation equation of the satellite orbit elements under both J2 and drag perturbations was derived based on the Gauss perturbation equation.
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.
基于C - W方程，推导了用直角坐标和轨道根数描述的远程导引段多冲量变轨段策略的方程，同时给出了求解方程组的迭代算法。
Based on the C-W equation, equations with both rectangular coordinates and orbital elements for the impulse maneuvers in long-distance guidance are derived.
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.
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.
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.
针对剩余扭矩方程求解中出现的“增根”问题，提出了一种简便的技术途径。
In order to avoid the "Augment of Root" of nonlinear equation, a simple technical method was proposed.
导出了带无限多个参数的有根平面植树和平面树的色和方程的精确表达式。
The explicit expressions of chromatic sum equations for rooted planted trees and planar trees with infinitive parameters are derived respectively.
当该方程有根时，则给出根的个数。
If this equation has roots, then the number of roots is given.
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.
基于相对轨道根数法，根据卫星相对运动方程，提出了“自然队形”的概念及队形设计的一般方法，并给出了具体的例子。
A concept of natural formation and a general RT design method are proposed based on the relative Orbital Element method and the relative motion equation in this paper. An example is given.
本文给出该方程在F中有根或没有根的条件。
In this paper, the author gives condition that this equation has roots or has no roots in F.
本文研究了平面上一般带根地图的色和与双色和，得到了这类地图的色和与双色和函数方程。
In this paper, we study the chromatic and dichromatic sum functions of rooted general maps on the plane. The chromatic and dichromatic sum function equations of such maps are obtained.
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.
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.
解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。
To solve the equation means to move and change the terms about without making the equation untrue, until the root of the equation is obtained, which is the value of unknown term.
基于常用的求解复函数方程根的算法，进行研究探讨。
This thesis deals with the research of algorithm which is applied to finding roots of complex functional equation.
应用推荐