拉格朗日运动方程

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。

In this dissertation, dynamic problems of 6-RTRT parallel robot including modeling of dynamics, analysis of velocity and acceleration, establishment of Lagrangian dynamic equation, computation of inertia force and driving torque are analyzed using influence coefficient method.

本文用运动影响系数法对6-RTRT并联机器人进行了动力学研究，完成了动力学建模，分析了速度和加速度，建立了拉格朗日动力学方程，并完成了惯性力和驱动力矩的计算。

Firstly, from Gauss' equations and relative motion equations, the relation of control impulse and relative motion was expressed as analysis formulas and simplified based on the near circular condition. By deeply analyzing the mechanism of impulses in each directions (radial, in-track and cross-track directions) effect on relative motion respectively, two maneuvers to establish formation flying are provided: one is to utilize the impulses in radial and cross-track directions, the other is to utilize the impulses in along-track and cross-track directions. Both of the two methods can establish satellite formation flying of any configuration. The method with impulses irradial and cross-track directions needs only 3 impulses, while the method with impulses in along-back and cross-track directions needs 4 impulses. Lastly, by an example of establishing a space-circle formation flying, two maneuvers were compared with each other in the amount of impulses and fuel consuming estimation.

首先由高斯型拉格朗日轨道摄动运动方程得到轨道坐标系中控制冲量与轨道根数偏差的关系，基于近圆轨道的条件简化并带入相对运动方程，得到控制冲量与相对运动的关系表达式；通过深入分析各个方向（径向、沿迹向与轨道面法向）的控制冲量对相对运动的影响，给出了分别用径向与轨道面法向控制冲量组合和沿迹向与轨道面法向控制冲量组合实现编队捕获的两种控制策略；最后给出了一个空间圆编队捕获实例，并从燃料消耗、施加冲量次数及捕获时间等角度对比研究了两种控制策略的特点。

For the plane wave of laser without pulse shape, we derive the express of electron trajectory by the relative Lorentz and energy equations. Note that the orbit of electron becomes a "fat-8" in the average rest frame. For the plane wave of Gaussian laser, we may know that, through relative Hamilton-Jacobi equation, electrons are accelerated in the front of pulse and decelerated backward. Whereas for the non-plane wave of Gaussian laser, we solve the Lorentz and energy equations by fourth order Runge-Kutta method.

对于无脉冲形状的激光平面波是从考虑了相对论效应的Lorentz方程和能量方程出发，得到了电子的运动轨迹方程表达式，在纵向平均速度参照系下该电子的轨迹呈现"8"字形；对于高斯型单色激光平面波是从相对论Hamilton-Jacobi方程出发，得到激光平面波在脉冲前沿加速电子而脉冲后沿减速电子，电子能量增益为零；而对于高斯型单色激光非平面波是从拉格朗日运动方程和能量方程出发，通过四阶Runge-Kutta法数值求解，得到电子在纵向有质动力、横向电场作用下加速电子，最后在强大的横向有质动力作用下从脉冲侧面散射出去，可以获得很大能量增益本文得到了相应的电子瞬时动量解析表达式。

Optimal liquidation ; intraday liquidity pattern ; Lagrange equation of motion ; Frobenius

最优变现；日内流动性模式；拉格朗日运动方程； Frobenius方法

Considering that the trade's price impact function includes the trade size and the liquidity discount of security market at that time,under the assumption that the risky asset's price follows the arithmetic Brown motion,and based on the none-shape,L shape or U shape of intraday liquidity patterns,this paper introduced the Lagrange equation of motion and the method of Frobenius,and found out the optimal intraday liquidation strategies of large security positions.

考虑到交易的价格影响是该时刻的交易量与市场流动性折扣的函数，假设风险资产价格服从算术布朗运动，以及分别在不考虑日内流动性模式，考虑L形和U形日内流动性模式的基础上，采用拉格朗日运动方程以及Frobenius方法，得到了大额风险头寸的日内最优变现策略。

With a rational dynamic model established on basis of the structural features and constraining conditions of the annular plate installation and through Duhamel＇s integral solution of Lagrange motion equation, the impact load and dynamic response of surface casing cementing unit induced from the cementing operation have been analyzed.

根据表层固井环板装置的结构特点和约束条件，建立了合理的力学模型，应用杜哈默积分求解拉格朗日运动方程的方法，对固并碰压状态下承受冲击载荷及其动力响应问题进行了分析。

With a rational dynamic model established on basis of the structural features and constraining conditions of the annular plate installation and through Duhamel's integral solution of Lagrange motion equation,the impact load and dynamic response of surface casing cementing unit induc.

根据表层固井环板装置的结构特点和约束条件，建立了合理的力学模型，应用杜哈默积分求解拉格朗日运动方程的方法，对固井碰压状态下承受冲击载荷及其动力响应问题进行了分析。

To investigate the dynamic stability of a two-degree-of-freedom manipulator as a system,differential equations of motion for this system were established on the basis of the Lagrange equation,and perturbed differential equations with period coefficients were derived for the period motion of this system by applying the perturbance theory.

为了研究两自由度机械手系统的动力学稳定性，基于拉格朗日方程给出了它的运动微分方程，并用扰动理论确定系统周期运动具有周期系数的扰动微分方程；根据F loquet理论对该系统扰动微分方程的平衡点的稳定性进行了分析，并用数值方法研究了平衡点失稳后的倍周期分岔过程。

Results show that the small vibration of this ideal model is non-simple harmonic,and the period of vibration in x direction and y direction are inverse ratio to the amplitude inverse ratio to the amplitude respectively,but influenced a little by them,and the waveform that coul.

本文应用拉格朗日方程方法研究了理想对称四弹性振子做二维运动的变化规律，得到其微小振动的控制方程，用数值解法求解出了振动方程，得到了振子运动的时程响应和轨迹图样。

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