Some aspects of continuous flow electrophoresis in microgravity

Zone electrophoresis is a highly efficient method of separating biological products. It is based on the differences of mobilities of ionized particles in an electric field. During the separation complications arise due to electro-osmosis or thermal convection generated by Joule heating.This paper analyses the hydrodynamical running of a continuous flow zone electrophoresis cell and shows the influence of specific parameters on the separation.The modelling of the flow structure of the buffer solution is developed. The equations and the corresponding boundary conditions are solved by finite difference method. The model established provides knowledge of the hydrodynamical perturbations generated by electro-osmosis and thermal free convection. The case of microgravity is considered.     

Deceleration and heating constrained footprint of shuttle vehicles

With increasing frequency in shuttle operation, it is of interest to have more than one or two landing fields within the boundary of the reachable area of the reentry vehicle. This boundary, called the footprint, depends on the aerodynamic characteristics of the vehicle and is severely restricted by the deceleration and heating constraints imposed upon the atmospheric reentry trajectory. This paper gives a general assessment of the footprint as a function of various deceleration and heating constraints. The difficulties in the computation of the three-dimensional reentry trajectories with optimal modulation in both the angle-of-attack and the bank angle are alleviated by the following devices: (a) nondimensionalizing of the equations of motion and use of the density as the altitude variable; (b) use of the classical integrals of the motion; (c) transformation of the adjoint variables into physical variables; and (d) spherical rotation of the coordinates.     

绳系卫星系统中的周期运动

在椭圆轨道上飞行的绳系卫星系统的重要特征是系绳的方向角具有周期性运动，称为驻环。不稳定的驻环导致全系统的不稳定性。本文给出系统运动的数学模型、距离速率控制方法、求解驻环的数值迭代算法、驻环的稳定性和吸引域以及控制参数平面上驻环存在的区界和计算机仿真结果     

基于数字仿真的再入飞行器滚转异常边界条件研究

提出了一种基于数字仿真的再入弹头滚转异常边界条件的确定方法。即：首先给出可精确描述考虑各种气动力（矩）系数、各种干扰源作用时的六自由度运动方程。针对各种干扰源及其组合作用，对某弹头的滚转异常现象作了大量的数字仿真。文中采用一种拟合方法，妥善处理了这些仿真结果，拟合出该弹头滚转异常边界条件的近似解析式     

Optimization of Multi-Orbit Transfers between Noncoplanar Elliptic Orbits

Using the maximum principle formalism, the problem of optimizing interorbital transfer between two noncoplanar elliptic orbits is reduced to solution of a boundary value problem for a system of ordinary differential equations. In order to solve the resulting boundary value problem numerically, the numerical homotopic method or modified Newton's method is used. When solving the boundary value problem, the right-hand sides of differential equations of motion are averaged numerically. Efficient software is developed, and a large number of optimal trajectories are calculated using it. As a result of analysis of these numerical data, new high-quality results are obtained. Specifically, a bifurcation of optimal solutions is found, the existence of critical inclination is demonstrated, and a partial classification of the structure of optimal control is performed.     

间接Legendre伪谱法的欠驱动航天器姿态运动轨迹跟踪

针对仅带有两组喷气推力器的非轴对称欠驱动刚性航天器,提出一种基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法。首先采用Legendre伪谱法(LPM)离线规划出系统的最短时间姿态机动参考轨迹。接着将实际运行轨迹与参考轨迹之间的偏差作为变量,根据Pontryagin极小值原理必要条件把系统姿态运动跟踪问题转化为一个两点边值问题(TPBVP)。最后采用 Legendre-Gauss-Lobatto(LGL)点将此两点边值问题离散转化为一个线性方程组来求解,避免了对传统Riccati微分方程的积分运算。数值仿真校验了本文基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法的有效性。     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: I

The problem of optimal control is considered for the motion of the center of mass of a spacecraft in a central Newtonian gravitational field. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems. Both the variants have a quaternion variable among the phase variables. In the first variant this variable characterizes the orientation of an instantaneous orbit of the spacecraft and (simultaneously) the spacecraft location in this orbit, while in the second variant only the instantaneous orbit orientation is specified by it. The suggested equations are convenient in the respect that they allow the general three-dimensional problem of optimal control by the motion of the spacecraft center of mass to be considered as a composition of two interrelated problems. In the first variant these problems are (1) the problem of control of the shape and size of the spacecraft orbit and (2) the problem of control of the orientation of a spacecraft orbit and the spacecraft location in this orbit. The second variant treats (1) the problem of control of the shape and size of the spacecraft orbit and the orbit location of the spacecraft and (2) the problem of control of the orientation of the spacecraft orbit. The use of quaternion variables makes this consideration most efficient. The problem of optimal control is solved on the basis of the maximum principle. Several first integrals of the systems of equations of the boundary value problems of the maximum principle are found. Transformations are suggested that reduce the dimensions of the systems of differential equations of boundary value problems (without complicating them). Geometrical interpretations are given to the transformations and first integrals. The relation of the vectorial first integral of one of the derived systems of equations (which is an analog of the well-known vectorial first integral of the studied problem of optimal control) with the found quaternion first integral is considered. In this paper, which is the first part of the work, we consider the models of motion of the spacecraft center of mass that employ quaternion variables. The problem of optimal control by the motion of the spacecraft center of mass is investigated on the basis of the first variant of equations of motion. An example of a numerical solution of the problem is given.     

导弹发射包线指数优化搜索仿真分析

以某型近距空空格斗导弹为例,针对传统计算导弹发射包线精度较低、模型复杂、解算耗时长问题,分析影响导弹发射包线形状大小的重要参数,建立简化的导弹六自由度运动模型。在搜索包线边界时,综合考虑八个重要运动参数,构建指数多项式函数,粗略估算初始搜索空间,避免搜索初始值的盲目性。在黄金分割法的基础上,提出指数优化搜索算法,结合每次搜索值的空间误差和函数值误差,更新并优化下一次搜索的黄金分割点。利用模型和Matlab仿真平台,解算弹道轨迹,利用搜索到的边界值进一步优化距离多项式系数,使初始计算值更接近真实边界值。实验表明,本文方法解算的弹道轨迹和发射包线与实战中数据基本吻合,有效地提高了计算精度;指数优化搜索算法有效减少了仿真计算次数,缩短了整体耗时。     

非线性三维变结构鲁棒自适应制导规律的研究

在三维球坐标系下建立了导弹与目标的相对运动模型,把目标加速度视为一类有界干扰,针对大机动目标提出了一种基于零化导弹与目标视线法向速度的三维变结构鲁棒自适应末制导律,并根据Lyapunov方法设计了参数自适应律.通过计算机数值仿真验证了导弹与目标的相对视线角速度最终趋向于零,验证了制导规律的正确性和有效性.     

微重力环境中重力梯度加速度引起的流体晃动运动

本文研究了关于旋转轴在贮箱的非对称轴上且远离贮箱的几何中心情况下，流体在微重力环境中由重力梯度加速度诱发的晃动特性，建立了问题的数学模型并对模型进行了数值模拟。以高级Ｘ射线天文物理实验卫星（简称ＡＸＡＦ─Ｓ）作为研究对象，获得了由旋转运动引起的重力梯度加速度的数学表达式。晃动问题的数值计算以与卫星固连的非惯性坐标系为基础，目的是寻求一种较为易处理且适合于流体力学方程的边界和初始条件。通过数值计算获得了流体作用于卫星贮箱上的力和力矩。