简化方程

The thermodynamic free energy on mixing and the Spinodal equation in ternary homopolymer blends were obtained by making plausible approximation based on Flory's equation of state theory.

本文运用Flory状态方程理论，对多元共混体系的热力学函数吉布斯共混自由能进行合理简化，并求得其Spinodal相图方程。

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。

This paper will deduce a group of new equations from general gas flow equation and Colebrook-White friction factor expression.

将气体流动基本方程与Colebrook White 摩擦阻力公式相结合推导出新的公式，大大简化了气体流动基本方程原来需要多次试算、迭代的计算过程，并且推导过程未加任何假设。

Recently, bas ed on Spitz's work, Porsani(1999) presented a half-step prediction filtering te chnique which simplified the two original prolix complex linear equation systems for calculating coefficients of prediction filter as a more simplex one so as t o reduce computational cost greatly.

最近，在Spitz工作的基础上， Porsani(1999年)提出了一种半步长预测滤波技术，它可以将原来用于求解预测滤波器系数的两组复杂的复线性系统方程简化为一组更为简单的复线性系统方程，从而大大降低了运算工作量。

The equations for the helicoid and cross section of a ballscrew are worked out and a numerical integral method for the computation of the moment of inertia of the cross section is proposed.

建立了滚珠丝杠的螺旋面方程及横截面方程，提出一种精确计算滚珠丝杠横截面惯性矩的数值积分法，计算结果表明，传统的简化方法将造成20％以上的计算误差。

Based on the theory of robotics, manipulator's kinematics equation is established and inverse kinematics analysis and calculation is made by algebraic solution after simplification, besides, Cartesian-space schemes, working space and singularities are also taken into account.

在机器人学的理论基础上，使用D-H方法建立了机械手的运动学方程；通过问题简化，利用代数解法，进行了逆运动学分析和计算，并对机械手进行了笛卡尔坐标轨迹规划，为后续控制系统的设计及机构运动仿真提供了依据；分析了机械手的工作空间、奇异性；介绍了建立机器人动力学方程的常用方法。

Using the Conservation Law of mass, momentum, energy in the form of Euler and equation of the thermodynamics, the interaction between the shock wave and the wall surface of the excavation roadway during the gas explosion is discussed.

文章建立了瓦斯爆炸冲击波的管道物理模型，利用Euler形式的动量、质量、能量守恒方程和热力学方程从理论上解析了瓦斯爆炸过程中爆炸冲击波与掘进巷道壁面相互作用中正反射和斜反射时波阵面上的各个参数，并给出了计算公式和简化公式。

In the low-low satellite to satellite gravity mission, the intersatellite range and range-rate data are the observable values, while the intersatellite acceleration can be derived from the range-rate through digital differential. Using acceleration data, people can avoid solving the variation equations of the satellite motion and simplify the observation equations. But on the other side, the digital differential will amplify the observation noises and finally affect the solved geopotential accuracy.

低低卫星跟踪卫星的观测量是两低轨卫星的星间距离或星间速度，星间加速度由星间速度通过数值微分导出，用星间加速度作为观测量可以避免解算卫星运动的变分方程，简化观测方程的建立，但数值微分会使观测噪声放大，从而影响重力位的解算精度。

The method of moments is an integral equation based numerical technique is to reduce the formal problem to a set of linear equations that can be solved by matrix inversion.

作为一种基于数字技术的积分方程，矩量方法用来将传统的问题简化为可以用矩阵转换来解决的一系列方程集。

The multiple method of scale is used to obtain the averaged equations in primary parameter resonance. From the averaged equations, the theory of normal form is applied to find the explicit formulas of normalform associated with a double zero and a pair of pure imaginary eigenvalues with the aid of the Maple program.

利用多尺度方法得出了主参数共振情况下的平均方程，利用Normal Form理论对具有双零特征值和一对纯虚特征值的平均方程进行了简化，得到了平均系统的Normal Form。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失