查询词典 equation of motion

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。

Based on the Timoshenko-Mindlin hypothesis and the Hamilton Principle, a set of governing equations of motion for the laminated non-circular cylindrical thick shells were founded.Using the Galerkin procedure,the Mathieu equation only with time variable was obtained,and this equation was solved by the method of increase harmonic balance.

基于Timoshenko-Midlin假设及Hamilton变分原理，建立了层合中厚非圆柱壳的非线性运动控制方程，采用伽辽金技术，得到仅含时间参数的Mathieu型方程，然后应用增量谐波平衡法进行求解。

For intramolecular electron transfer reactions in solution,the fluctuations of the intramolecular vibrational modes are much faster than that of solvent mode.Thus,the reaction-diffusion equation is commonly used to describe the motion of solvent,with a sink function to treat the vibrational high-frequency mode.Based on this theory-so -called the Sumi-Marcus theory,we proposed an imaginary-time split operator approach to solve the reaction-diffusion equation.The approach is applied to evaluate the intermolecular ET rate between oxazine 1 and N,N-dimethlaniline.By measuring the two average survival times of the donor state probability and the rate constant in long time limit,the full kinetics of the ET is revealed with a variety of sink functions.

对于扩散控制的溶液中的电子转移反应，分子内振动模的运动比溶剂运动快很多，Sumi-Marcus理论提出用反应扩散方程(reaction-diffusion equation)处理溶剂的扩散运动，而分子内的振动用sink函数来表示，我们基于此理论发展了用虚时间分裂算符的方法(imaginary-time Split operator approach)解反应扩散方程，并将其应用于嗪1(oxazine 1，OX1)和N，N-二甲基苯胺分子之间的电子转移反应，Sink函数采用几种不同的微扰表达式，通过计算得到给体几率衰减的两种平均速率和长时间极限下的速率常数，揭示了该体系电子转移过程中的一些动力学性质。

The noise frequency modulation signal was particularly analyzed. The Fokker-Planck equation of noise frequency modulation was presented and the Motion-Group Fourier Transform was used by converting the partial differential equation into the variable coefficient homogenous linear differential equations. Then the solutions were given by using the peano-baker series. So the probability density function of noise frequency modulation in the filter was given. On the basis of the probability density function the stochastic resonance of noise frequency modulation signal is analyzed.

首先建立了噪声调频干扰信号通过脉冲压缩雷达中频滤波器后所满足的福克尔－普朗克方程，然后利用群移傅立叶变换（Motion-Group Fourier Transform，MGFT）将此偏微分方程化成了变系数齐次线性微分方程组，并利用Peano-Baker级数法给出了该方程组的解，最后得到了噪声调频干扰信号通过脉冲压缩雷达中频滤波器后的概率密度函数，在此基础上研究了噪声调频干扰信号造成的随机共振现象。

Chapter 7. Make use of the unified field equation studied intrinsic magnetic field for planets, got that the magnetic induction equation is satisfied with the motion of planetary inside matter.

第七章 利用统一场方程研究了行星的固有磁场，也得到了行星内部物质运动所应满足的磁感应方程。

The motion equation of a particle is reduced to the nonlinear differential equation with a weak_periodic modulation by sine_squared potential.

利用正弦平方势把粒子运动方程化为具有外周期弱调制的非线性微分方程，并利用Melnikov方法分析了系统出现Smale马蹄的临界条件。

In this paper difference equation of motion fr om one point to another point on the earth is derived from the geodesic equation on the earth and spherical trigonometry formulas. Some difference track formul as of a maneuvering object are also given.

以大地椭球三角形模型为基础，利用地球表面二点间最短路径的大地线方程和球面三角形的有关公式，建立了由地球表面一点运动到另一点的差分运动方程，同时也给出了在进行航向机动时的差分运动轨迹。

In this paper differ ce equation of motion fr om one point to another point on the earth is derived from the geodesic equation on the earth and spherical trigonometry formulas. Some difference track formul as of a maneuvering object are also given.

以大地 椭球三角形模型为基础，利用地球表面二点间最短路径的大地线方程和球面三角形的有关公式，建立了由地球表面一点运动到另一点的差分运动方程，同时也给出了在进行航向机动时的差分运动轨迹。

In the study of the Lagrange stability of impact motion, we give some conditions of the bouncing solution of the asymptotically linear equation which is bounded or unbounded. Outside of a large disc, using the symplectic transformation of the Hamilton system to estimate the iteration of the successor map. Applying the Moser's small twist theorem, we get the invariant curves and then give the proof of the bouncing solutions which is bounded. We will estimate the successor map of the equation directly for proving the unboundedness of the bouncing solutions.

在碰撞运动的Lagrange稳定性的讨论中，给出了渐近线性方程碰撞解有界或无界的条件，在充分大的圆盘外，通过Hamilton系统的辛坐标变换的角度平均来估计后继映射的迭代，应用Moser小扭转定理得到不变曲线从而给出在一定条件下碰撞解有界的证明，碰撞解无界性的证明将采用直接估计后继映射的方法给出。

The muscle is simulated by elastic foundation and put into the wall of managing having a viscid condition and the motion of fluid by the linear momentum equation and the continuity equation, and therefore, the governing equations are derived.

由肌肉弹性假设为弹簧来描述管壁运动，也加入了管壁具有黏滞性的条件，而且配合流体的线动量方程以及连续条件，推导出统御方程式。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。