擾蕩方程，[物] 擾動方程
From the perturbation equation of the shaker stability, the conditions of self synchronous stable running are derived.
利用振動篩的穩定性擾動方程得到了同步穩定運轉條件。
The temperature sensitivity of the frequency as a function of quartz crystal anisotropy is presented by the perturbation equation due to the temperature change.
利用波擾動方程，分析研究了聲表面波器件頻率-溫度敏感性與石英晶體各向異性參數之間的關系。
The advantage of this method in solving the perturbation equation is also discussed.
并讨論了用這種方法求解攝動方程的優越性。
In chapter three, we dealed with some nonlinear perturbation equation by use of Yan's direct approach for soliton perturbation.
第三章，運用顔家壬教授發展的微擾直接法處理了一些含微擾的非線性方程。
The effects of WOB fluctuation of drill string on the wellbore trajectory are analyzed by using stochastic finite element method and perturbation equation.
借助隨機有限元方法和攝動方程初步分析了鑽壓波動對井眼軌迹的影響。
The thermal blooming involves the paraxial wave equation and density perturbation equation, which are detailed analyzed from Maxwell's equations and hydrodynamic equations.
從近軸波動方程和等壓近似下空氣密度擾動方程出發，讨論熱暈所涉及的方程；
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氣膜壓強和非結構三角網格的有限元法解壓強攝動方程，得到氣膜的剛度系數和阻尼系數矩陣。
The variation equation of the satellite orbit elements under both J2 and drag perturbations was derived based on the Gauss perturbation equation.
基于高斯攝動方程，推導了衛星在同時考慮J2和大氣攝動情況下的軌道根數變化方程。
Based on the model of fuzzy patter recognition, the weight perturbation transfer equation of recognizes matrix is presented.
研究了模糊模式識别、聚類和動态規劃的權重靈敏度分析問題。
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.
用近代統計力學研究成果——積分方程理論和微擾理論簡要評述了電解質和非電解質溶液的國内外研究進展。
A surface equation of state for ionic surfactant aqueous solutions is also developed by combining perturbation theory and pressure equation .
将微擾理論與壓力方程相結合，建立了離子表面活性劑水溶液的表面狀态方程。
The frequency stability, amplitude stability and harmonic content can be deduced from the second order perturbation solution of that equation.
方程的二階近似解顯示出非線性效應對振蕩頻率穩定度、振幅穩定度及波形正弦純度的影響。
The simulated results are analyzed and compared with those predicted from perturbation theory and integral equation theory under mean spherical approximation.
模拟結果與微擾理論和平均球近似積分方程理論的預測值進行了比較。
This paper is concerned with oscillation property of solutions of a class of second-order nonlinear differential equation with perturbation.
研究了一類二階非線性攝動微分方程解的振動性質。
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.
本文應用簡并态微擾理論和球諧函數的性質，得到久期方程中非零微擾矩陣元普遍表達式。
In this paper, the parabolic equation with boundary perturbation is considered. Using discussion of the solvability, the perturbed solution of original problem is obtained.
本文研究了具有邊界攝動的抛物型方程。利用可解性的讨論，得到了原問題的攝動解。
I tackle the perturbation problem of the nonlinear Schrodinger equation because of its importance.
本人首先用此方法處理了自散焦非線性薛定谔方程的孤子微擾問題。
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.
第二部分同樣用微擾理論來研究濾波器的作用，導出了頻域濾波孤子傳輸系統的脈沖演化方程；
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.
本文介紹了用于分析遊離基反應的前線軌道的微擾分子軌道理論的普通方程。
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橢圓型偏微分方程奇異攝動問題。
A variable length ****** pendulum model is introduced, elementary analysis and perturbation analytic solution of nonlinear differential equation for parametric resonance are presented.
采用可變長度單擺的力學模型對秋千振蕩給出初等分析，采用微擾近似法導出了秋千的非線性參數共振解析解， 并進行了讨論。
Then a control method considering the J2 perturbation based on Encke's linearization equation is proposed to maintain the relative motion of the constellation.
進而導出了帶有J2項攝動的環繞星相對運動方程，并給出了基于慣性笛卡爾坐标系運動學變量的相對軌道控制方法。
Without the perturbation of noise, the determinate dynamic equation could display the character of Hopf bifurcation.
研究發現在沒有環境擾動的作用下，體系的宏觀确定性動力學方程可以呈現霍普夫分岔特性；
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.
這種方法不要求精确地求解，它在每一次疊代求解牛頓方程時都在牛頓方程右端加上一個擾動項，從而達到提高計算效率的目的。
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.
首先采用攝動法從理論上推導出時滞動力系統的分叉響應方程，再采用數值模拟的方法研究了時滞參數對系統分叉響應的影響。
In this paper we constructed an exponentially fitted difference scheme for singular perturbation problem of hyperbolic-parabolic partial differential equation.
本文對雙曲-抛物偏微分方程奇異攝動問題構造了一個指數型拟合差分格式。
This paper deals with the existence and nonexistence of solutions for a critical semilinear polyharmonic equation with a non-negative perturbation.
讨論了帶非負擾動的臨界非齊次多重調和方程多解存在性和非存在性。
擾動方程（Perturbation Equation）的詳細解釋
1. 術語分解與核心定義
2. 擾動方程的數學内涵
擾動方程是攝動理論（Perturbation Theory）的核心工具，用于量化微小擾動對系統的影響。其一般形式可表示為：
$$
L_0(u_0) = 0 quad text{（未擾動系統方程）}
$$
$$
L_0(u_0 + delta u) + epsilon L_1(u_0 + delta u) = 0 quad text{（含擾動項的系統方程）}
$$
其中，$epsilon$為小參數，$delta u$為擾動引起的變量修正量（來源：國際期刊《應用數學與力學》研究論文）。
3. 應用場景與實例
4. 理論意義與擴展
擾動方程不僅提供近似解析解的方法（如正則攝動法），還為數值模拟中的線性化處理奠定基礎。其局限性在于僅適用于弱非線性系統，強擾動需借助其他方法（如多尺度分析）（來源：《非線性動力學》權威教科書）。
"Perturbation equation"（擾動方程）是數學和物理學中用于描述系統在微小幹擾（擾動）下行為變化的方程。它屬于攝動理論（perturbation theory）的核心工具，主要應用于難以直接求解的複雜系統，通過引入微小參數進行近似分析。以下是詳細解釋：
擾動方程通常基于原系統方程（未受幹擾的狀态）構建。當系統受到微小外部影響或參數變化時，原方程會被修改為： $$ mathbf{F}(x) + epsilon mathbf{G}(x) = 0 $$ 其中：
通過分析$epsilon$趨近于零時的解，可近似得到受擾動系統的行為。
以簡諧振動為例，原方程為： $$ mfrac{dx}{dt} + kx = 0 $$ 加入阻尼擾動後，擾動方程為： $$ mfrac{dx}{dt} + cfrac{dx}{dt} + kx = 0 $$ 其中$c$是微小阻尼系數（對應$epsilon c$）。
如需進一步了解具體領域的應用，可參考攝動理論教材或相關論文。
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