On stability of a rotating spacecraft partially filled with liquid: The case of a single cavity

The problem of stability of a rotating spacecraft with a cavity partially filled with liquid to a small depth is considered with regard to the distinction in angular velocities of spacecraft and liquid rotation and their variability (the modes of the spacecraft’s stationary rotation, spin-up, and rotation deceleration). The regions of stability (in space of the characteristic parameters of an object) are found, and mathematical simulating of the disturbed motion is carried out.     

失重条件下对称充液陀螺的不稳定行为研究

对于质心固定的，充满粘性均匀液体的旋转对称陀螺在失重条件下绕对称长轴旋转态的小扰动不稳定及其极限行为进行了研究，所给出的定理3比以往的不稳定定理[4]为强，且反映的信息量多很多。关于初始大扰动后的渐近行为，对文[8]已给出但未严格证明的两条定理给出了严格证明，它由定理1和定理2所描述。     

Biaxial Mode of Rotation of a Satellite in the Orbit Plane

A mode of motion of a satellite with respect to its center of mass is studied, which is called the biaxial rotation in the orbit plane. In this mode of rotation, an elongated and nearly dynamically symmetric satellite rotates around the longitudinal axis, which, in turn, rotates around the normal to the plane of an orbit; the angular velocity of rotation around the longitudinal axis is several times larger than the orbital angular velocity, deviations of this axis from the orbit plane are small. Such a rotation is convenient in the case when it is required to secure a sufficiently uniform illumination of the satellite's surface by the Sun at a comparatively small angular velocity of the satellite. The investigation consists of the numerical integration of equations of the satellite's motion, which take into account gravitational and restoring aerodynamic moments, as well as the evolution of the orbit. At high orbits, the mode of the biaxial rotation is conserved for an appreciable length of time, and at low orbits it is destroyed due to the impact of the aerodynamic moment. The orbit altitudes and the method of constructing the initial conditions of motion that guarantee a sufficiently prolonged period of existence of this mode are specified.     

一种用于快速跟踪视线的空间拦截器姿态控制方法

以空间拦截器的纵轴在中、末制导段要求指向目标的视线，按最小空间角距旋转，作为跟踪目标的姿态定向的假想坐标系，形成本体坐标系相对假想坐标系的误差四元数。由拦截器的转动角速度分量与误差四元数作为状态反馈构造稳态姿态控制的数学模型。为了得到姿态控制所需的变控制力矩，运用PWPF调制器对常值推力姿控发动机的稳态和脉冲工作状态进行调制，构造所谓的“数字变力矩”控制器，实现对姿态的连续控制。仿真计算结果表明，该方法是实际可行的。     

航天密封舱设备安装精度仿真分析方法

针对航天密封舱设备安装精度受密封舱内压影响却没有实用的理论预示方法,提出了仿真分析设备安装精度的方法。该方法根据有限元结构仿真分析得到的位移,导出设备的安装精度;另外,提出了精测数据的分析方法,使设备的安装精度变化规律更明显,更容易看出设备旋转的旋转轴、旋转方向、旋转角度,也使精测数据与仿真数据的对比更容易,可为验证仿真分析的准确性提供前提条件。利用一个算例对文章提出的仿真分析方法进行了验证。结果表明,仿真分析方法能准确地确定设备安装角度变化的旋转轴和旋转方向,计算出的旋转角度值与精测结果也基本一致。     

轴系回转轴线指向误差测量方法

回转轴线指向误差是扫描机构的重要性能指标之一,对遥感成像质量有明显影响。针对回转轴线无法直接精确测量的问题,提出了基于平面反射镜、电子自准直仪的测量系统。在详细分析平面反射镜法线与回转轴线间关系的基础上,对测得的镜面法线指向数据进行傅里叶级数展开,通过零次项去除和一次谐波分量误差分离处理,得到真实的回转轴线指向误差。利用该方法对某扫描轴系实物进行了测量,结果表明:该方法测得的回转轴线误差为39″,满足系统的指标要求,相对于常规处理方法在精度和准确度上有所提高。     

One method of gravitational attitude control of a rotating satellite

The mode of spinning up a low-orbit satellite in the plane of its orbit is studied. In this mode, the satellite rotates around its longitudinal axis (principal central axis of the minimum moment of inertia), which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around the longitudinal axis is several tenths of a degree per second. Gravitational and restoring aerodynamic moments were taken into account in the equations of satellite’s motion, as well as a dissipative moment from eddy currents induced in the shell of the satellite by the Earth’s magnetic field. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape and nongravitational external moments are introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasistationary rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. We propose to consider such quasistationary rotations as unperturbed motions of the satellite in the spin-up mode.     

Convection of liquid with internal heat release in a rotating container

The convection of heat-generating fluid in a rotating horizontal cylinder is experimentally investigated. The threshold of convection excitation, the structure of convective flows and the heat transfer in the cylinder depending on the heat release capacity, liquid viscosity and aspect ratio of the cavity are studied. It is found that the average convection is excited by the thermovibrational mechanism —the gravity force, rotating in the cavity frame, produces the oscillations of non-isothermal fluid relative to the wall, which in turn result in excitation of mean convective flows. It is shown that the structure of convective flows depends on the dimensionless velocity of rotation. At relatively low rotation velocity the convection develops in the form of a periodic system of vortices regularly distributed along the cylinder axis. The threshold of excitation (critical value of vibration parameter) of three-dimensional vortex structures grows with rotation velocity. Above some definite rotation velocity the convection develops as two-dimensional rolls parallel to the axis of rotation. The threshold of two-dimensional structures excitation does not depend on the rotation velocity. Besides the structure of thermal convective flows the analysis of the relatively weak currents generated by the inertial waves below the threshold of convection is performed.     

美国小行星俘获任务及其启示

小行星俘获(ACR)任务是美国Keck空间研究中心发起的一项深空探测任务。该任务计划选定一颗近地小行星,通过口袋式抓捕系统对其实施抓捕,并于2025年左右将其带回近月空间。文章介绍了ACR任务的内容和系统设计,具体包括:航天器总体构型、抓捕分系统、探测识别分系统和控制与推进分系统;对小行星抓捕的目标探测与识别、旋转匹配、抓捕、消旋、轨道转移等核心操作。基于ACR任务,提出了空间目标俘获技术的需求与应用、抓捕航天器系统设计的启示;基于我国目前的技术研究情况,总结分析了发展空间目标俘获任务所需的关键技术,如大功率柔性太阳翼、长时间大范围轨道机动、目标探测与识别、快速机动、目标抓捕与消旋。     

The Motion of Coaxial Bodies of Varying Composition on the Active Leg of Descent

The motion of a spacecraft (SC) with double rotation and variable mass on the active leg of its descent is considered. The SC consists of two coaxial bodies. The coaxial scheme is used for gyroscopic stabilization of the SC longitudinal axis by the method of partial spin-up. The equations of spatial motion of coaxial bodies of varying composition are derived and approximate solutions for the angles of spatial orientation are found. The condition of decreasing amplitude of nutation oscillations is obtained, which allows the estimation of efficiency of the stabilization by partial spin-up. The errors in the magnitude and direction of the vector of braking thrust are also determined.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 3, 2005, pp. 224–232.Original Russian Text Copyright © 2005 by Aslanov, Doroshin, Kruglov.     

带充液腔的自旋卫星稳定性问题

本文应用Pfeiffer的思想讨论带轴对称充液腔的卫星系统自旋稳定性。本方法的基本思想为将轴对称腔内的液体旋度平均化,使之与空间位置无关,由此将液体的无限自由度问题离散化为有限自由度问题,从而用线性理论讨论系统的自旋稳定性。用这方法,本文讨论了带充液腔的非轴对称卫星系统、带充液腔的双自旋卫星系统的自旋稳定性,给出了它们的自旋稳定性判据。此外,本文还给出了一些带有不同形状腔体的卫星系统自旋稳定域图,为实际工程设计人员提供理论参考。     

Application of a magnetohydrodynamic element in the control loop of a rotating spacecraft with a spike antenna

The problem of stabilization of a rotating spacecraft with a flexible spike antenna located along the axis of spacecraft rotation is considered. A magnetohydrodynamic element is used as a final-control element in the control loop of spacecraft attitude, and the solar direction sensor serves as a measuring device. At the first stage of investigation, the problem of stability is considered for stationary and non-stationary modes of rotation of the spacecraft with a flexible antenna and with a cavity partially filled with a low-viscosity liquid.     

Periodic motions of a satellite-gyrostat relative to its center of mass under the action of gravitational torque

We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.     

测量不确定的充液航天器自适应鲁棒容错控制

针对三轴稳定充液航天器控制系统中同时存在外部未知干扰,参数不确定,测量不确定和执行器部分失效故障的鲁棒容错姿态机动控制问题进行研究。首先将部分充液贮箱内的晃动液体燃料等效为粘性球摆模型,采用动量矩守恒定律推导出航天器的刚-液耦合动力学方程。然后将变结构控制策略结合范数自适应估计算法设计了自适应鲁棒容错控制器,其中设计的范数自适应控制算法用于有效估计由测量不确定产生的集总扰动的未知上界;自适应估计算法则用于有效估计贮箱内的液体晃动位移变量。提出的控制策略不依赖精确的故障信息,并且在故障信息值不确定的情况下可以实现期望的姿态机动任务。基于Lyapunov稳定性分析方法证明了容错闭环系统状态变量的一致最终有界性。采用数值方法验证了所提控制方法的有效性和鲁棒性。     

On dynamics of a plasma ring rotating in the magnetic field of a central body: Magneto-gyroscopic waves. Problems of stability and quantization

Based on a mathematical model described in [1], some new aspects of the dynamics of a thin planar plasma ring rotating in the magnetic field of a central body are considered. The dipole field is considered assuming that the dipole has a small eccentricity, and the dipole axis is inclined at a small angle to the central body’s axis of rotation. Emphasis is placed on the problem of stability of the ring’s stationary rotation. Unlike [1], the disturbed motion is considered which has a character of eddy magneto-gyroscopic waves. The original mathematical model is reduced to a system of finite-difference equations whose asymptotic analytical solution is obtained. It is demonstrated that some “elite” rings characterized by integral quantum numbers are long-living, while “lethal” or unstable rings (antirings) are associated with half-integer quantum numbers. As a result, an evolutionally rife rotating ring of magnetized plasma turns out to be stratified into a large number of narrow elite rings separated by gaps whose positions correspond to antirings. The regions of possible existence of elite rings in near-central body space are considered. Quantum numbers determining elite eigenvalues of the mean sector velocity (normalized in a certain manner) of a ring coincide with the quantum numbers appearing in the solution to the Schrödinger equation for a hydrogen atom. Perturbations of elite orbits corresponding to these quantum numbers satisfy the de Brogli quantum-mechanical condition. This is one more illustration of the isomorphism of quantization in microcosm and macrocosm.     

充液航天器液体晃动等效力学模型的建立

在考虑液体表面张力影响液体晃动求解的基础上,利用动力学方程等价准则,建立了三轴定向充液卫星在二维平动和二维摆动扰动作用下的空间摆等效力学模型,并对两种情况下等效摆的主要参数进行了计算和比较。结果表明,考虑表面张力时,液体的晃动特性对航天器姿态控制系统稳定性有不利影响。     

Lift force acting on the cylinder in viscous liquid under vibration

The averaged lift force acting on a solid in viscous liquid in case of translational or rotary vibrations of a cavity is experimentally investigated. Experiments are performed with a heavy cylinder; different types of vibrations, translational and rotational, are investigated. It is found that the vibrations excite the mean lift force which could provide the suspension of solid even in gravity field. The repulsion lift force acts on the body near the walls of the vibrating cavity. It is caused by the viscous hydrodynamic interaction of oscillating body with the wall and is significant at a distance comparable with the thickness of Stokes layer. The intensification of vibration results in the excitation of tangential lift force, which is caused by the brake of the symmetry of the body's oscillations with respect to the cavity wall. In case of rotary vibrations the lift force of high intensity manifests itself in the bulk of the cavity due to the interaction of body with the oscillating shear flow. The mean dynamics of the solid body in a cavity under the rotary vibrations is determined by the combined action of two averaged vibrational effects—levitation of the body in the oscillating shear flow and hydrodynamic interaction of the body with the wall. In case of translational vibrations the dynamics of the solid is mainly determined by interaction with the walls. The experiments demonstrate that the vibrations have strong mean effect on the bodies in liquid; they could be used for efficient control of solid inclusions in microgravity and must be taken into account in space experiments and technologies.     

Maneuver planning of a rigid spacecraft with two skew control moment gyros

The attitude maneuver planning of a rigid spacecraft using two skew single-gimbal control moment gyros (CMGs) is investigated. First, two types of restrictions are enforced on the gimbal motions of two skew CMGs, with each restriction yielding continuous control torque along a principal axis of the spacecraft. Then, it is proved that any axis fixed to the spacecraft can be pointed along an arbitrary inertial direction by at most two sequent rotations around the two actuated axes. Given this fact, a two-step eigenaxis rotation strategy, executing by the two single-axis torques respectively, is designed to point a given body-fixed axis along a desired direction. Furthermore, a three-step eigenaxis rotation strategy is constructed to achieve an arbitrary rest-to-rest attitude maneuver. The rotation angles required for the single-axis pointing and arbitrary attitude maneuver schemes are all analytically solved. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithms.