扰荡方程，[物] 扰动方程
From the perturbation equation of the shaker stability, the conditions of self synchronous stable running are derived.
利用振动筛的稳定性扰动方程得到了同步稳定运转条件。
The temperature sensitivity of the frequency as a function of quartz crystal anisotropy is presented by the perturbation equation due to the temperature change.
利用波扰动方程，分析研究了声表面波器件频率-温度敏感性与石英晶体各向异性参数之间的关系。
The advantage of this method in solving the perturbation equation is also discussed.
并讨论了用这种方法求解摄动方程的优越性。
In chapter three, we dealed with some nonlinear perturbation equation by use of Yan's direct approach for soliton perturbation.
第三章，运用颜家壬教授发展的微扰直接法处理了一些含微扰的非线性方程。
The effects of WOB fluctuation of drill string on the wellbore trajectory are analyzed by using stochastic finite element method and perturbation equation.
借助随机有限元方法和摄动方程初步分析了钻压波动对井眼轨迹的影响。
The thermal blooming involves the paraxial wave equation and density perturbation equation, which are detailed analyzed from Maxwell's equations and hydrodynamic equations.
从近轴波动方程和等压近似下空气密度扰动方程出发，讨论热晕所涉及的方程；
The pressure perturbation equation is solved by finite element method with unstructured ******** grids for film stiffness and damping coefficients.
采用算子分裂法求解气膜压强和非结构三角网格的有限元法解压强摄动方程，得到气膜的刚度系数和阻尼系数矩阵。
The variation equation of the satellite orbit elements under both J2 and drag perturbations was derived based on the Gauss perturbation 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。
Based on the model of fuzzy patter recognition, the weight perturbation transfer equation of recognizes matrix is presented.
研究了模糊模式识别、聚类和动态规划的权重灵敏度分析问题。
A brief review by the progress of advanced statistical mechanics, integral equation and perturbation theory for electrolyte and non-electrolyte solutions in recent years is presented.
用近代统计力学研究成果——积分方程理论和微扰理论简要评述了电解质和非电解质溶液的国内外研究进展。
A surface equation of state for ionic surfactant aqueous solutions is also developed by combining perturbation theory and pressure equation .
将微扰理论与压力方程相结合，建立了离子表面活性剂水溶液的表面状态方程。
The frequency stability, amplitude stability and harmonic content can be deduced from the second order perturbation solution of that equation.
方程的二阶近似解显示出非线性效应对振荡频率稳定度、振幅稳定度及波形正弦纯度的影响。
The simulated results are analyzed and compared with those predicted from perturbation theory and integral equation theory under mean spherical approximation.
模拟结果与微扰理论和平均球近似积分方程理论的预测值进行了比较。
This paper is concerned with oscillation property of solutions of a class of second-order nonlinear differential equation with perturbation.
研究了一类二阶非线性摄动微分方程解的振动性质。
The prevalent formula for nonzero perturbation matrix in the secular equation is gained by the perturbation theory in degenerate state and property of spherical harmonics function.
本文应用简并态微扰理论和球谐函数的性质，得到久期方程中非零微扰矩阵元普遍表达式。
In this paper, the parabolic equation with boundary perturbation is considered. Using discussion of the solvability, the perturbed solution of original problem is obtained.
本文研究了具有边界摄动的抛物型方程。利用可解性的讨论，得到了原问题的摄动解。
I tackle the perturbation problem of the nonlinear Schrodinger equation because of its importance.
本人首先用此方法处理了自散焦非线性薛定谔方程的孤子微扰问题。
Secondly, we have stu***d the effect of filters by the use of perturbation theory and derived the evolution equation of the soliton pulse in the presence of sliding frequency.
第二部分同样用微扰理论来研究滤波器的作用，导出了频域滤波孤子传输系统的脉冲演化方程；
It is proved in this paper that the perturbation molecular orbital (PMO) equation can be used to analyse the frontier molecular orbitals(FMO)in the Free Radical Reactions.
本文介绍了用于分析游离基反应的前线轨道的微扰分子轨道理论的普通方程。
By applying finite element method, this paper discussed a singular perturbation problem of elliptic partial differential equation, and constructed a special finite element subspace.
本文用有限元方法研究椭圆型偏微分方程奇异摄动问题。
A variable length ****** pendulum model is introduced, elementary analysis and perturbation analytic solution of nonlinear differential equation for parametric resonance are presented.
采用可变长度单摆的力学模型对秋千振荡给出初等分析，采用微扰近似法导出了秋千的非线性参数共振解析解， 并进行了讨论。
Then a control method considering the J2 perturbation based on Encke's linearization equation is proposed to maintain the relative motion of the constellation.
进而导出了带有J2项摄动的环绕星相对运动方程，并给出了基于惯性笛卡尔坐标系运动学变量的相对轨道控制方法。
Without the perturbation of noise, the determinate dynamic equation could display the character of Hopf bifurcation.
研究发现在没有环境扰动的作用下，体系的宏观确定性动力学方程可以呈现霍普夫分岔特性；
This method does not solve equations exactly. In each iteration, it adds a perturbation to the right side of Newton equation to reduce the computation workload.
这种方法不要求精确地求解，它在每一次迭代求解牛顿方程时都在牛顿方程右端加上一个扰动项，从而达到提高计算效率的目的。
Perturbation method is used to obtain the bifurcation equation with time-delays, and numerical method is utilized to analyze the effect of time-delays on the steady state response.
首先采用摄动法从理论上推导出时滞动力系统的分叉响应方程，再采用数值模拟的方法研究了时滞参数对系统分叉响应的影响。
In this paper we constructed an exponentially fitted difference scheme for singular perturbation problem of hyperbolic-parabolic partial differential equation.
本文对双曲-抛物偏微分方程奇异摄动问题构造了一个指数型拟合差分格式。
This paper deals with the existence and nonexistence of solutions for a critical semilinear polyharmonic equation with a non-negative perturbation.
讨论了带非负扰动的临界非齐次多重调和方程多解存在性和非存在性。
扰动方程（Perturbation Equation）的详细解释
1. 术语分解与核心定义
2. 扰动方程的数学内涵
扰动方程是摄动理论（Perturbation Theory）的核心工具，用于量化微小扰动对系统的影响。其一般形式可表示为：
$$
L_0(u_0) = 0 quad text{（未扰动系统方程）}
$$
$$
L_0(u_0 + delta u) + epsilon L_1(u_0 + delta u) = 0 quad text{（含扰动项的系统方程）}
$$
其中，$epsilon$为小参数，$delta u$为扰动引起的变量修正量（来源：国际期刊《应用数学与力学》研究论文）。
3. 应用场景与实例
4. 理论意义与扩展
扰动方程不仅提供近似解析解的方法（如正则摄动法），还为数值模拟中的线性化处理奠定基础。其局限性在于仅适用于弱非线性系统，强扰动需借助其他方法（如多尺度分析）（来源：《非线性动力学》权威教科书）。
"Perturbation equation"（扰动方程）是数学和物理学中用于描述系统在微小干扰（扰动）下行为变化的方程。它属于摄动理论（perturbation theory）的核心工具，主要应用于难以直接求解的复杂系统，通过引入微小参数进行近似分析。以下是详细解释：
扰动方程通常基于原系统方程（未受干扰的状态）构建。当系统受到微小外部影响或参数变化时，原方程会被修改为： $$ mathbf{F}(x) + epsilon mathbf{G}(x) = 0 $$ 其中：
通过分析$epsilon$趋近于零时的解，可近似得到受扰动系统的行为。
以简谐振动为例，原方程为： $$ mfrac{dx}{dt} + kx = 0 $$ 加入阻尼扰动后，扰动方程为： $$ mfrac{dx}{dt} + cfrac{dx}{dt} + kx = 0 $$ 其中$c$是微小阻尼系数（对应$epsilon c$）。
如需进一步了解具体领域的应用，可参考摄动理论教材或相关论文。
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