变分方程

For the purpose of extending the applicability of the coupling method to the bidimensional exterior steady Oseen problem, we will introduce a smooth artificial boundary separating an interior inhomogeneous region from an exterior homogeneous region .The solution in the exterior region is represented by an integral equation over the artificial boundary.

为了将这种耦合方法应用于二维外部定常的Oseen问题，我们人为的引入一条光滑的边界，将内部非均匀区域和外部均匀区域分离，外部区域的解可以由人工边界上的积分方程来描述，此积分方程同内部区域的速度-压力变分形式结合为耦合变分形式，我们则可以使用有限元的方法求解此耦合变分方程。

This paper discusses a variation equation problem in a class of singular stochastic control with stopping time,gives its solution under two different conditions,which is a one order continuous differentiable and concave function,and gives the exact form.

讨论了一类带停时的奇异型随机控制问题中的一个变分方程问题，并且在两种不同的情况下给出了该变分方程的解，即为一阶连续可导凹函数，并在两种情况下给出了此函数的具体形式。

By using a first integral particular solution of variational equations is obtained and an example is given.

给出相对论自治 Birkhoff系统的变分方程，研究它们的解，并利用第一积分得到变分方程的特

Variational equations of motion of each flexible link are derived under Jourdain variational principle, and then the mixed algebraic-differential equations of flexible multibody systems are obtained with the kinematic constraint conditions.

用Jourdain速度变分原理建立各机械臂的动力学变分方程，在此基础上根据各物体之间的运动学约束关系，建立柔性多体系统的微分代数混合动力学方程。

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

Based on Lagrangion function in the form of a volume integration of liquid pressure superposed on the standard Lagrange function (kinetic energy minus potential energy), corresponding to liquid subsystem and structure subsystem respectively, the nonilnear coupled dynamic equations of the coupling system are established by means of variation principle and Lagrangion equation.

对液体子系统和结构子系统分别得到压力体积分形式的Lagrange函数和标准形式Lagrange函数，由变分方程和Lagrange方程可以建立系统的动力学方程。

Based on the two phase anisotropic model this paper analyses and presents the dynamic equations of elastic wave propagation, the Galerkin variational equation, and the finite element equation in two phase anisotropic media.

基于双相各向异性介质模型，首先推导了双相各向异性介质中弹性波传播的动力学方程及其Galerkin变分方程和有限元运动方程，然后给出了孔隙弹性波方程的有限元数值解法以及二维双相PTL介质中波场模拟的人为吸收边界条件。

To avoid the trouble to construct the basis functions, we introduce a Lagrange multiplier into the variational formulation to replace the constraint condition for the basis.

本文采用同样的思路用Galerkin 边界元方法求解带有约束条件的与第一类Fredholm 间接边界积分方程等价的变分方程，为避免构造基函数时约束条件的限制，我们采用Lagrange 乘子法，把约束条件放入变分方程中去，形成扩展的变分方程，用线形单元离散后求解。

Then we obtain equation of variation by aciculate variation.Finally we obtain the inequality of variation of optional control.

然后利用针状变分求出系统的变分方程，从而得到了最优控制满足的变分不等式。

The variational equations are established for holonomic nonconservative dynamical systems in the high-dimensional ex-tended phase space.

建立了高维增广相空间中完整非保守力学系统的变分方程，并利用系统的正则方程和变分方程证明，可由第一积分直接构造系统的积分不变量，并举例说明结果的应用。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。