级数解

A typical Mathieu equation subject to harmonic excitation is acquired by means of the theory of linear vibration. By using integral transformation, the series solutions to the Mathieu equation are obtained.

根据线性振动理论对系统运动微分方程组进行分析，得到了一个受简谐激励的Mathieu方程，通过积分变换，得到了Mathieu方程的级数形式解。

Based on the elastic theory of large deflection and by taking into account the variation of the axial force and its effects on bending deformation of the drillstring in vertical section,the vibration of the drillstring induced by fluctuating weight-on-bit is described by a parametrically excited system.A Mathieu equation describing the system is established by Galerkin Method.By extending the solution into a Fourier series,the curves of dynamic bifurcation values and the dynamically unstable regions surrounded by the curves are presented.

基于弹性大变形理论，考虑到轴力沿钻柱轴线的变化及其对钻柱弯曲变形的影响等因素，将受自重作用的铅垂井段钻柱在波动钻压激励下的振动转化为一个参数激励系统，用Galerkin方法首次得到了描述此系统的Mathieu方程，并通过将方程的解展成富里叶级数的方法，得到了该振动系统的动力分岔值曲线及其所包围的动力不稳定区。

Under suitable conditions, firstly, using the expansion method of power series, the reduced solution and formal outer solution are constructed.

在一定的假设下，首先，利用幂级数形式展开方法，构造了原问题的外部解。

The natural twist vibration equation is set up by making use of the constitutive relation of nonlinear material.

利用非线性材料的本构关系，建立了非线性材料圆杆的扭转固有振动方程，然后采用傅立叶级数法求得了圆杆扭转固有振动的所似解，通过实例计算讨论分析了非线性材料圆杆的扭转固有振动特性。

Then solving the equation by using Neumann series direct integration method .

提出了求解这类动力学方程数值解的Neumann级数－直接积分法。

Based on this, this paper develops the modal series method, expounds its mathematic foundation and theory system, and compares it with the linear modal analysis and the method of norm form of vector fields.

开发了基于模态级数法的HVDC/AC互联电力系统分析软件包，通过此软件可以得到系统的非线性响应，获得非线性系统零输入响应的近似闭式解，进行系统模态分析、非线性模态交互作用分析，并为控制系统设计提供有价值的特征信息。

The orthogonal expansion of the solution of the rotating disk motion equation is analyzed, and the stability of the system that includes the controller and the dynamics of sensor and actuator are analyzed.

本文通过对旋转圆盘运动方程解的正交级数展开的分析，由此在考虑控制器、作动器和传感器的动态特性情况下，分析了旋转圆盘振动主动控制系统的稳定性，指出了系统失稳的条件。

The computer simulations show the validity of the new method. The orthogonal expansion of the solution of the rotating disk motion equation is analyzed, and the stability of the system that includes the controller and the dynamics of sensor and actuator are analyzed.

本文通过对旋转圆盘运动方程解的正交级数展开的分析，由此在考虑控制器﹑作动器和传感器的动态特性情况下，分析了旋转圆盘振动主动控制系统的稳定性，指出了系统失稳的条件。

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。

In order to solve this model, perturbation method is employed and the solution is expanded into a series in powers of perturbation parameter.

利用小扰动方法处理了任意形状非均质油藏不稳定渗流问题，将解表达成关于扰动参数的无穷幂级数形式。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。