查询词典 structure equations

Moreover, for the treelike system with prescribed motion and the non-treelike system with closed-loop, the generalized coordinates aren't independent completely. Only the dynamical equations of the system and the constrain equations resulting from the prescribed motion and the closed-loop are combined to form DAEs, it can be solved.

另外，对于有指定运动的树系统或带有闭环的非树系统，系统的广义坐标是不完全独立的，系统的动力学方程要与指定运动或系统切断所附加的约束方程一起组成微分--代数方程组才能求解。

The derivatives of the nonsmooth equations are computed to make the generalized derivative matrix nonsingular. Then the nonsmmoth damped Newton method is used to solve them.Analytic solutions of the KdV equation with variable coefficients: Shallow water wave problems belong to problems of free surface wave, and can be molded by the nonsmooth equations model given above in principle.

在前面建立的非光滑方程组数学模型和固定网格法基础上，利用广义导数的概念给出了求解渗流自由面的一种新方法-----非光滑阻尼牛顿法，该法是对非光滑方程组求导，适当的处理广义导数矩阵使其非奇异，利用非光滑牛顿法求解。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

This paper systematically discussed the definition, nature and calculation of two kinds of generalized inverse matrix related to the compatible linear equations, and their relations with the compatible linear equations.

本论文系统地论述与相容线性方程组相关2种广义逆矩阵的定义、性质和计算，以及与相容线性方程组的关系。

The two kinds of symmetries in holonomic and non-holonom-ic mechanical systems,i.e.symmetries of differential equations of motion(ab-breviated as SDEM)and symmetries of Noether-type,and interrela-tions among all kinds of symmetries are investigated.The necessary and suffi-cient conditions of SNT to be SDEM are found out.It is pointed out thatSDEM have distinct geometric properties which are equivalent to the geodesiccharacteristic of differential equations of motion and geodesic deviation.

文中研究了完整与非完整力学系统的两类对称性，即运动微分方程的对称性和Noether型对称性，以及各种对称性之间的相互关系，确定了Noether型对称性为运动微分方程对称性的充分必要条件，并指出运动微分方程的对称性具有明确的几何性质，即它等价于运动微分方程的测地性质以及测地偏离性质。

The topics covered in these sections are the geometric interpretation of systems of linear equations, the classification of finite symmetry groups in two and three dimensions, the exponential of a matrix and its application to solving systems of first order linear differential equations with constant coefficients, and Hurwitz's theorem on the composition of quadratic forms.

这些条文所涉及的主题是线性方程组的几何解释，在两个和三个有限对称群的分类方面，一个矩阵及其应用，以解决一阶常系数线性差分方程，系统指数赫尔维茨定理在二次形式组成。

Now that we have discussed the meaning of a graphical solution of a system of simultaneous equations and the method of plotting a l , we are in a position to find graphical solutions of systems of linear equations.

由于 我们已讨论过联立方程组的图解法和绘制直线的方法，我们就能够找出线性方程组的图解法。

The coupling effect between elastic deformation and the rigid motion was concerned in the dynamic equations. At the same time, the flexible manipulators were assumed as Euler-Bernoulli beams, the elastic deformation of the manipulator was represented by modality truncation equations, both elastic and gravitational potential energy were considered to calculate the total energy for whole system, therefore the finial dynamic modeling is more accurate and simple than others published.

该方法考虑了柔性机械臂刚体运动和弹性变形之间的耦合影响，并将柔性机械臂假设为一段Euler-Bernoulli梁处理，将弹性变形用截断模态方程表示，同时考虑了弹性势能和重力势能的影响，得到的双连杆柔性机械臂的动力学模型具有模型准确、结构简单等特点。

Firstly, four geometric loop equations are set up by using vector method in complex number fields. Secondly, three constraint equations are used to construct the Dixon resultants, which is a 6×6 matrix and contain two variables to be eliminated. Extract the greatest common divisor of two rows and two columns of Dixon matrix and compute its determinant to obtain a new equation. This equation together with the forth constraint equation can be used to construct a Sylvester resultant.

首先使用矢量法和复数法建立4个几何约束方程式；再使用Dixon结式法对3个方程式构造一个含有2个变元的6×6 Dixon矩阵，提取其中2行列元素的公因式，将新矩阵的行列式展开后得到二元高次多项式方程，该方程与剩下一个方程使用Sylvester结式消去一变元，得到一元高次方程。

Maxwell's equations group in fact was already found in the basic experimental laws of electromagnetic phenomena, as well as a single magnetic pole does not exist on the facts and the integrated displacement current assumptions, using an international system of units, these equations can be written as: DivDW =ρ or DW =ρ(1) kiDivBq = 0 or Bq = 0 (2) kiCurlEBq =- Zt or × EqkZ =- BqZt (3) ZCurlHDWDW = jE Zt, or × HW = jE Zkt (4) Z-type in the Curl, and Div were vector operator curl and divergence, Micro-k points for the Hamiltonian operator, in the rectangular coordinate system,= iZZEkx jEy kqz, iE, jE, kq along Zx, y, z-axis unit vector, a vector for any AW are × AW = CurlAW, kAW = DivAW; DW for the electric displacement, Bq for the magnetic induction intensity, Eq, and HW, respectively i field and electric field strength, jY for the conduction current density,ρ the charge density for free.

麦克斯韦方程组实际上是当时已发现的电磁现象的基本实验定律以及单个磁极不存在的事实和位移电流假设的综合，采用国际单位制，这些方程式可写成：DivDW＝ρ或DW＝ρ（1）kiDivBq＝0或Bq＝0（2）kiCurlEBq＝－Zt或×EqkZ＝－BqZt（3）ZCurlHDWDW＝jE＋Zt或×HW＝jE＋Zkt（4）Z式中Curl和Div分别为矢量算符旋度和散度，为哈密顿微k分算符，在直角坐标系中，＝iZZEkx＋jEy＋kqz，iE，jE，kq是沿Zx、y、z轴的单位矢量，对任一矢量AW有×AW＝CurlAW，kAW＝DivAW；DW为电位移，Bq为磁感应强度，Eq和HW分别为电i场和磁场强度，jY为传导电流密度，ρ为自由电荷密度。

If you were not , and OS X just booted normally, have no fear.

如果你没有，和OS X刚刚启动通常，没有恐惧。

I only want to preserve our all .

我只想保存好我们的一切