卫星编队飞行轨道和姿态控制研究

卫星编队飞行是一种卫星应用的新概念,通过一系列造价更便宜的小卫星的分布式合作,代替大卫星实现复杂功能．在编队飞行一些应用中,要求受控卫星对目标卫星保持要求的相对位置和姿态以观察目标卫星的特定面,特别的,目标卫星可能是失效的．研究在近地轨道如何控制追踪星在失效的目标卫星附近飞行以追踪目标卫星特定面 的问题,给出了相对姿态和一阶近似的相对轨道动力学方程．基于线性反馈和Liapunov稳定性理论设计了控制策略．进一步的,考虑目标卫星转动惯量的不确定性,通过自适应控制的方法,获得正确的转动惯量比率．数值仿真算例验证了该控制方法的有效性．     

具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析

研究了一类具有缺陷的不可压缩超弹性材料球壳的径向对称运动问题,该类材料可以看作是带有径向摄动的均匀各向同性不可压缩的neo-Hookean材料．得到了描述球壳内表面运动的二阶非线性常微分方程,并给出了方程的首次积分．通过对微分方程的解的动力学行为的分析,讨论了材料的缺陷参数和球壳变形前的内外半径的比值对解的定性性质的影响,并给出了相应的数值算例．特别地,对于一些给定的参数,证明了存在一个正的临界值,当内压与外压之差小于临界值时,球壳内表面随时间的演化是非线性周期振动;当内压与外压之差大于临界值时,球壳的内表面半径随时间的演化将无限增大,即球壳最终将被破坏．     

一种便于摄动分析的编队飞行卫星相对运动的描述

定义了一组参数来描述卫星编队飞行的相对运动,称为相对轨道要素．利用它可以方便地分析摄动对相对轨道构形的影响以及卫星编队队形的几何特点．首先,对相对轨道要素给予了详细的推导,指出当主星偏心率为小量时,在主星轨道坐标系中相对轨道是一椭圆柱和一平面相交所得的交线,用描述该椭圆柱和平面的参数即可确定相对轨道构形,进而提出了相对轨道要素．其次,利用相对轨道要素对相对轨道进行地球扁率摄动分析,指出相对轨道构形的变化由两部分组成:一是椭圆柱的漂移导致相对轨道中心的漂移,二是平面法线的章动和进动引起相对轨道平面转动,同时还给出了地球扁率摄动下相对轨道构形漂移率及转动率的解析公式．最后,针对J2摄动分析了卫星编队相对轨道构形的变化以及相对轨道构形的漂移量和转动量．     

地球引力场对卫星有摄运动的一种计算方法

本文应用Delaunay变量,从理论力学的哈密顿方程出发,通过正则变换求解了地球引力摄动对卫星运动轨道的影响,导出卫星位置和速度随时间的变化关系.     

为什么大行星可以同时有顺行和逆行卫星

本文用圆型限制三体问题的Jacobi积分来建立一个能确定卫星是否稳定的测检函数.凡是对其主行星所作的瞬时椭圆轨道要素已知的卫星都可检定其稳定性.对于作准圆形轨道运动的卫星,我们可用电子计算机来求出它的稳定域,这域的界面是一个近似的扁椭球面.这闭面所包围的空间比“引力作用球”和其相应的卫星区的“Hill曲面”要小得多.由于卫星对其主行星的相对动能表示式对顺行和逆行轨道两者形式相同,所以两者可以在卫星的稳定域中同时存在.     

动载荷下不可压缩超弹性球形薄膜的若干定性性质

对于由横观各向同性不可压缩的Rivlin-Saunders材料组成的球形薄膜,研究了薄膜的内、外表面在周期阶梯载荷作用下的轴对称变形的非线性动力学特性．通过令球形结构的厚度趋近于1,得到了近似描述薄膜径向对称运动的二阶非线性常微分方程．详细讨论了解的定性性质．特别地,给出了球形薄膜随时间的运动产生非线性周期振动的可控性条件,证明了在某些情形下周期振动的振幅会出现“∞”型同宿轨道以及周期振动的振幅会出现不连续增长现象,并给出了相应的数值模拟．     

卫星编队飞行中C-W方程与轨道根数法的比较

目前卫星编队飞行动力学与控制的研究得到了广泛的重视,这些研究的理论主要是基于描述卫星相对运动的Clohessy-Wiltshire(C-W)方程。但根据特例及定性分析,表明C-W方程在初始条件的选取、解的周期性等方面与实际情况不符,从星的能量也不守恒。以卫星轨道根数为基础,提出了卫星编队飞行中的相对轨道根数法,克服了C-W方程的局限性,物理概念清楚,应用范围广,解的周期性成为自然结论。在主星为小偏心率的情况下,得到了简化的相对运动方程。最后对两种方法进行了比较,指出了C-W方程的局限性及其原因。     

固体平板上超薄水膜去湿润过程的分子动力学模拟

运用分子动力学模拟研究固体表面超薄水膜的失稳和破裂过程．结果表明薄膜中小扰动将失稳,并在初始阶段线性增长．但固体和液体的相互作用对扰动的初期增长影响较小．最小厚度的下降导致薄膜发生破裂．此后破裂边缘以一定的动态接触角后退．与宏观理论预测一致,边缘半径随时间的变化与时间平方根成正比．若固液相互作用较强,将引起破裂时间延迟,动态接触角减小,固体表面附近的液体密度增加．     

在重力场和磁场影响下自旋刚性航天器的周期运动

考虑重力场和磁场对轴对称航天器本体的影响，研究其质心在圆形轨道上的运动,通过降低系统的运动方程数，并将它变成为一个带电粒子在电磁场作用下的平面运动．确认系统运动是稳定的，并通过Liapunov全纯积分定理，构建其近似的周期运动.     

固定合作规模网络的平均路径长度

本文提出了一种特殊的合作网络,称之为固定合作规模网络．我们重点研究了这类网络的平均路径长度,通过建立微分方程,得到平均路径长度的增加速度近似与网络规模的对数成正比．     

The effect of gravity on flow past a semi-circular cylinder with a constant pressure wake

The flow past a semi-cylinder with a trailing wake region is considered. In the absence of gravity the only known high Reynolds number solutions have tangential separation from the body and a cusped shape at the back of the wake. This flow can be a simple model for several situations, including the classical approximation of a constant pressure wake and the flow past an object with a region of trapped fluid of different density (or an air cavity) attached on the downstream side. Here we relax the assumption of high flow speeds to examine the effects of gravity. It is shown that there are situations in which a stagnation point can form either on the body or at the tail of the wake and that there is a minimum velocity beneath which a cavity will not form. Non-uniqueness in the parameter space is found in certain cases.     

非均匀温度场中组合热超弹性球体的动态孔穴生成

在有限变形动力学的框架下,研究了在非均匀温度场中组合热超弹性球体,在表面均布拉伸死载荷作用下的动态孔穴的生成和增长问题．首先建立了相应的非线性数学模型,利用换元积分方法求得了孔穴半径与外加载荷之间的一个精确的微分关系,并进行了数值计算,得到了不同温度下球体中孔穴生成时的临界载荷和分叉曲线．考察了参数对孔穴生成与增长的影响,并与相应的静态结果进行了比较．结果表明孔穴是以一个有限的半径突然出现的,且随时间的演变孔穴半径呈现周期性的非线性振动;当温度升高,临界值降低,同时在相同的条件下动态临界载荷低于静态临界载荷．     

Optimization methods for pipeline transportation of natural gas with variable specific gravity and compressibility

In this paper, the problem of flow maximization in pipeline systems for transmission of natural gas is addressed. We extend previously suggested models by incorporating the variation in pipeline flow capacities with gas specific gravity and compressibility. Flow capacities are modeled as functions of pressure, compressibility and specific gravity by the commonly-used Weymouth equation, and the California Natural Gas Association method is used to model compressibility as a function of specific gravity and pressure. The sources feeding the transmission network do not necessarily supply gas with equal specific gravity. In our model, it is assumed that when different flow streams enter a junction point, the specific gravity of the resulting flow is a weighted average of the specific gravities of entering flows. We also assume the temperature to be constant, and the system to be in steady state. Since the proposed model is non-convex, and global optimization hence can be time consuming, we also propose a heuristic method based on an iterative scheme in which a simpler NLP model is solved in each iteration. Computational experiments are conducted in order to assess the computability of the model by applying a global optimizer, and to evaluate the performance of the heuristic approach. When applied to a wide set of test instances, the heuristic method provides solutions with deviations less than 10% from optimality, and in many instances turns out to be exact. We also report several experiments demonstrating that letting the compressibility and the specific gravity be global constants can lead to significant errors in the estimates of the total network capacity.     

一维六方准晶双材料中圆孔边共线界面裂纹的反平面问题

研究了一维六方准晶双材料中圆孔边不对称共线界面裂纹的反平面问题。利用Stroh公式和复变函数方法得到了声子场和相位子场耦合作用下的复势函数,给出了裂纹尖端应力强度因子和能量释放率的解析表达式。通过数值算例,讨论了圆孔半径和裂纹长度对应力强度因子的影响,以及耦合系数、声子场应力和相位子场应力对能量释放率的影响。结果表明:当圆孔半径不变时,应力强度因子随右裂纹长度的增大趋向稳定值。当相位子场应力取一定值时,能量释放率达到最小值,说明特定的相位子场应力可以抑制裂纹的扩展。     

Die Bestimmung von Halbleiterparametern in Ge-PIN-Detektoren mit der Elektronensonde

Summary In this paper we report the use of the scanning electron beam technique for a measurement of the ambipolar diffusion length, the surface recombination velocity and the electric field distribution in Ge-Li-PIN-Diodes. A simple relation between the diffusion length and the photovoltage induced by the electron beam is derived. The diffusion length as a function of temperature shows a strong increase with decreasing temperature. This fact limits our method to temperatures above –80°C. A measurement of the electric field distribution is demonstrated for the case of double injection in PIN-Diodes with an extended intrinsiczone. The conductivity modulation caused by the electron beam, at constant current in forward direction, results in a change in the terminal voltage which is proportional to the square of the electric field strength at the injection point.     

空泡溃灭时的流场

本文在Rayleigh方法的基础上,对具有表面张力含汽型空泡的溃灭进行了分析.导出空泡溃灭时空泡半径、泡壁速度及溃灭压力与时间的函数关系,并由此给出速度场及压力场的数值解.     

Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software

A hollow sphere made from functionally graded piezoelectric material (FGPM) such as PZT_4 has been considered. One-dimensional analytical method for electro-thermo-mechanical response of symmetrical spheres is used. For asymmetric three-dimensional analysis, ANSYS finite element software is employed in this study. Loading is combination of internal and external pressures, a distributed temperature field due to steady state heat conduction and a constant electric potential difference between its inner and outer surfaces for analytical solution. In three-dimensional solutions closed and open spheres with different boundary conditions subjected to an internal pressure and a uniform temperature field are studied. All mechanical, thermal and piezoelectric properties except the Poisson’s ratio are assumed to be power functions of radius. It has been found from analytical solution that the induced radial and circumferential stresses of an imposed electric potential is similar to the residual stresses locked in the homogeneous sphere during the autofrettage process of these vessels. It has been concluded from the three-dimensional analysis that the magnitudes of effective stresses at all node points are higher for the clamped-clamped boundary condition and are lower for the simply-simply supported condition.     

One-dimensional viscoelastic fluid model where viscosity and normal stress coefficients depend on the shear rate

We study the unsteady motion of a viscoelastic fluid modeled by a second-order fluid where normal stress coefficients and viscosity depend on the shear rate by using a power-law model. To study this problem, we use the one-dimensional nine-director Cosserat theory approach which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. Integrating the equation of conservation of linear momentum over the tube cross-section, with the velocity field approximated by the Cosserat theory, we obtain a one-dimensional system. The velocity field approximation satisfies both the incompressibility condition and the kinematic boundary condition exactly. From this one-dimensional system we obtain the relationship between average pressure and volume flow rate over a finite section of the tube with constant and variable radius. Also, we obtain the correspondent equation for the wall shear stress which enters directly in the formulation as a dependent variable. Attention is focused on some numerical simulation of unsteady/steady flows for average pressure, wall shear stress and on the analysis of perturbed flows.     

Numerical solution of the two- dimensional equations of laminar flame propagating down a cylindrical tube

In the present paper a system of premixed laminar flame freely propagating, at constant pressure, down a cylidrical tube, having constant cool wall temperature, was formulated and numerically solved. Single-step Arrhenius kinetics and average transport properties were used for a simulated propane-air mixture. The solution method was based on linearizing the nonlinear terms in the equations, using the Picard method, and solving line by line to cover the integration field. Iteration then proceeded with varying degrees of underrelaxation until convergence was obtained. The solution yielded the flame speed and structure at any tube diameter. The flame structure revealed the wall cooling effect on the flame at various diameters.