格朗

Based on FLAC,a conclusion is obtained that it is not necessary for Lagrange method to solve through motion equation from both the angle of calculation convergence and physical meaning.

通过对FLAC的研究，得出一个结论：拉格朗日方法无论从计算收敛的角度还是从物理意义的角度，基于运动方程求解都是不必要的。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables, and the state and costate variables inside the time interval were approximated by Lagrange interpolation. Nonlinear optimal control problems were replaced by nonlinear equations through dual variable principle, and the symplectic algorithm for solving nonlinear optimal control problems can be obtained at the same time.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables,and the state and costate variables inside the time interval were approximated by Lagrange interpolation.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

In the numerical analysis, us-pw formation of dynamic consolidation equation and cyclic elasto-plastic constitutive model is used. Using updated Lagrangian method, large deformation of liquefied ground is considered.

在数值分析过程中，采用us-pw形式的动力固结方程和循环弹塑性本构关系，并引入更新的拉格朗日格式以适应土体液化后的大变形。

A deterministic global optimization algorithm based on Lagrangian dual is proposed for solving the nonconvex quadratic programming with nonconvex quadratic constraints, which is often encountered in technical design and operational research.

针对带有非凸二次函数约束的非凸二次规划问题，提出了一个基于拉格朗日对偶的确定型全局优化算法，这类优化算法可广泛应用于工程设计和非线性系统的鲁棒稳定性分析等实际问题中。

Considering that the temperature gradient through thickness is much higher than that through width and length of plate, in this model, the governing equation of heat transfer was simplified as a one dimensional differential equation, and the series function solution for temperature is established in Lagrangian coordinate setting.

在该模型中，考虑到轧件厚度方向的温度梯度远大于沿宽度和长度方向的温度梯度，因而将热传导方程简化为一维微分方程，基于拉格朗日坐标建立了温度场的级数解法。

Helene orbits in Dione's leading Lagrange point.

Helene的轨道是在Dione的拉格朗日前点上。

At first, we introduce in detail relativistic mean-field theory, where a common Lagrangian density is presented. Starting with this Lagrangian density, we can obtain the Dirac equation and Klein-Gordon equations for nucleon and meson field by using Euler-Lagrangian equation.

本文首先详细介绍了相对论平均场理论的一些公式推导，给出了常用的一般的相对论平均场的拉格朗日量，从这个拉氏量出发，利用Euler-Lagrange方程就可导出核子与介子场的运动方程。

With Lagrange multiplier ,Dirichlet boundary conditions are imposed along the essential boundaries.

在有限元三维20结点单元构成的空间网格上构建流形覆盖和权函数，采用拉格朗日乘子法施加位移约束条件，推导了分析静态问题的计算列式。

Based on the basic theoryof non linear finite element, the author of the paper set up the double non linearfinite element equation based on the updated Lagrangefor mutations forthe 8-node degenerate shell element and considering the nonlinear of geometryand the nonlinear of materials.

本文根据非线性有限元的基本理论，采用基于修正的拉格朗日法描述的八节点超参数壳体单元，考虑几何非线性和材料非线性，推导建立了双重非线性有限元方程，结合混合强化本构关系，编制了非线性有限元计算程序。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新