Dynamics of an axisymmetric satellite under the action of gravitational and aerodynamic torques

Dynamics of attitude motion of an axisymmetric satellite moving in a circular orbit under the action of gravitational and aerodynamic torques is investigated. All equilibrium positions of the satellite in the orbital coordinate system are determined numerically, and sufficient conditions of stability of the equilibrium positions are derived.     

Dynamics of a gyrostat satellite with the vector of gyrostatic moment in the principal plane of inertia

Dynamics of a gyrostat satellite moving along a circular orbit in a central Newtonian field of force is investigated. In a particular case, when the gyrostatic moment vector lies in one of the satellite’s principal central planes of inertia, all positions of equilibrium are determined, and the conditions of their existence are analyzed. Also determined are bifurcation values of dimensionless parameters, at which the number of equilibrium positions changes. As a result of analysis of the generalized energy integral, for each equilibrium orientation the sufficient conditions of stability are derived. Evolution of the regions where the sufficient conditions of stability are valid is investigated under variation of the system’s dimensionless parameters.     

Dynamics of an axisymmetric gyrostat satellite under the action of gravitational moment

Dynamics of an axisymmetric gyrostat satellite moving in the central Newtonian force field along a circular orbit is investigated. All equilibrium positions of the gyrostat satellite in the orbital coordinate system are determined, and the sufficient stability conditions of equilibrium positions are derived.     

Gravity-oriented satellite dynamics subject to gravitational and active damping torques

The dynamics of the rotational motion of a satellite moving in the central Newtonian field of force over a circular orbit under the effect of gravitational and active damping torques, which depend on the satellite angular velocity projections, has been investigated. The paper proposes a method of determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of damping coefficients and principal central moments of inertia. The conditions of their existence have been obtained. For a zero equilibrium position where the axes of the satellite-centered coordinate system coincide with the axes of the orbital coordinate system, the necessary and sufficient conditions for asymptotic stability are obtained using the Routh–Hurwitz criterion. A detailed analysis of the regions where the conditions of the asymptotic stability of a zero equilibrium position are fulfilled have been obtained depending on three dimensionless parameters of the problem, and the numerical study of the process of attenuation of satellite’s spatial oscillations for various damping coefficients has been carried out. It has been shown that there is a wide range of damping parameters from which, by choosing the necessary values, one can provide the asymptotic stability of satellite’s zero equilibrium position in the orbital coordinate system.     

Stability of motion of a space vehicle under constantly acting disturbances

The attitude stability of an Earth-orbiting satellite experiencing aerodynamic torque is studied. This is accomplished by applying the theory of total stability (or, stability under constantly acting disturbances) to the equations of motion. The satellite is gravity-gradient stabilized and a damping torque is incorporated. The aerodynamic torque results from the presence of two flat panels attached to the cylindrical body of the vehicle. This perturbing torque is treated as an additive disturbance in Euler's equations of motion. A Lyapunov function is constructed and then used in an appropriate theorem on stability under constantly acting disturbances. Explicit expressions are thereby found for bounds on a hypothetical initial condition (a rotation from the Earth-pointing equilibrium) and on the aerodynamic torque, so that if these disturbances are less than their respective bounds then the resulting attitude motion of the satellite will not exceed a pre-assigned value. These bounds depend on that pre-assigned value, and on the physical parameters of the satellite. The design implications of these bounds are then discussed.     

The Dynamics of a Satellite-Gyrostat with a Single Nonzero Component of the Vector of Gyrostatic Moment

The dynamics of a satellite-gyrostat moving in the central Newtonian force field along a circular orbit is studied. In the particular case when the vector of gyrostatic moment is parallel to one of the satellite’s principal central axes of inertia, all the equilibrium states are determined. For each equilibrium orientation, sufficient conditions of stability are obtained as a result of the analysis of the generalized energy integral, and necessary conditions of stability are determined as a result of analysis of the linearized equations of motion. The evolution of regions of validity for the conditions of stability of equilibrium positions are studied in detail depending on the parameters of the problem. All the bifurcation values of the parameters at which qualitative changes of the regions of stability take place are determined.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 283–294.Original Russian Text Copyright © 2005 by Sarychev, Mirer, Degtyarev.     

Electrodynamic stabilization of earth-orbiting satellites in equatorial orbits

A satellite with electrodynamic stabilization system is considered. Based on the method of Lyapunov functions, sufficient conditions of the asymptotic stability of direct equilibrium position of this satellite in the orbital coordinate system under perturbing action of a gravitational moment are obtained. These conditions allow one to ensure a rational choice of parametric control coefficients depending on parameters of the satellite and its orbit.     

基于参数化外形的通用大气飞行器建模与分析

提出了一类翼身组合升力体外形通用大气飞行器(Common Aero Vehicle, CAV)的参数化外形建模方法,采用气动工程预估方法计算CAV的气动系数,拟合得到能用于再入飞行器制导与控制仿真的气动模型,并通过分析,得到该模型静稳定性、气动效率及气动控制特性等方面的结论。结合飞行器再入飞行的运动方程,选取平衡工作点,基于小扰动线性化模型得到系统特征根分布来分析其稳定性,发现固定姿态的滑翔飞行时系统有正半平面极点,需主动控制调节;为了分析机动性,提出了以星下点轨迹曲率求取CAV转弯半径的方法,可快速获取机动性评估与参考指标,结果表明,该模型具有较好的转弯机动能力。     

Modeling of the aerodynamic moment acting upon a satellite

We consider the issues of modeling the moments of aerodynamic forces acting upon a satellite with gravitational system of stabilization. It is assumed that satellite orbits are almost circular with heights in the range 550–750 km. Simplified analytical expressions are suggested for the aerodynamic moment in the case when a satellite moves in the regime of gravitational orientation. Accuracy of the obtained expressions is estimated to be compared with that of expressions derived under the assumption of constant coefficient of frontal resistance. An analysis is made of short-periodic variations of the atmosphere density occurring due to orbital motion of a satellite. It is demonstrated that these variations can result in a substantial change of the aerodynamic moment, and their approximation by a truncated Fourier series is suggested. Estimates of the accuracy of the suggested approximation are given.     

高精度遥感卫星力矩补偿技术

基于建立的卫星姿态动力学模型,对高精度遥感卫星有效载荷工作时载荷运动产生的干扰力矩及其对卫星姿态的影响进行了研究。提出了反馈控制＋力矩补偿的方法,给出了力矩补偿的设计。仿真结果表明：在补偿时延小、补偿精度高条件下利用补偿轮进行力矩补偿,可提高卫星的姿态稳定度,使其满足卫星成像时的姿态控制指标要求。     

磁力矩器强度计算分析及尺寸优化设计

磁力矩器是卫星的重要执行机构。为了保障其使用的可靠性,文章运用有限元分析的方法,计算磁力矩器的力学特性,同时采用材料力学和有限元计算的方法,对其进行优化设计,降低最大应力。计算结果表明:不均匀的温度场导致较大热应力。磁力矩器的危险部位主要集中在支架底座与螺栓接触面处,通过尺寸优化设计可以减小此处的应力。     

On plane oscillations of a pendulum with variable length suspended on the surface of a planet’s satellite

The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We discuss how the change in length of a pendulum can be used to compensate its oscillations. We wrote equations of motion, indicated a rule for the change in length of a pendulum, at which it has equilibrium positions relative to the coordinate system rotating together with the Moon and Earth. We study the necessary conditions for the stability of these motions. Chaotic dynamics of the pendulum is studied numerically and analytically.     

星载大型空间天线的一种解耦控制方法

针对星载大型空间可展开天线与卫星平台之间的动力学耦合问题提出一种三自由度驱动与测量机构用于连接天线臂与卫星平台。该机构以驱动电机来控制天线臂转动,通过角度传感器对天线臂转角的测量来实现反馈控制,同时在卫星姿态控制系统中引入前馈控制进行反作用力矩补偿,实现卫星平台与天线之间的解耦控制、抑制天线的振动、提高卫星姿态控制系统的性能。通过姿态稳定状态下卫星-天线系统解耦动力学模型的建立、控制系统的设计、姿态控制的仿真分析,表明解耦机构能大幅增加天线振动的阻尼,有效提高卫星稳定性和天线指向精度。     

反作用飞轮电机换相力矩波动抑制协同控制方法

针对反作用飞轮电机换相所产生的非理想力矩影响卫星姿态控制精度的问题,采用永磁无刷直流电机绕组感生电势、相电流和电磁转矩的解析计算方法得到了反作用飞轮电机的换相力矩波动最小化条件,提出了基于该最小化条件的换相力矩波动抑制高动态协同控制方法,抑制反作用飞轮电机三种运行状态下的换相力矩波动.试验结果表明,电动状态下换相力矩波动减小了12%、可控能耗制动和反接制动状态下换相力矩波动减小了90%以上,验证了该方法的可行性和有效性.     

考虑星-箭动力耦合作用结构瞬态响应分析

利用直接激励法，对火箭发射过程中考虑星箭动力耦合作用的卫星结构瞬态响应问题进行了求解。给出了最大动压、一二级分离前和分离后三种工况下卫星结构的加速度响应历程。该方法克服了大质量法和惯性载荷法瞬态响应计算中的载荷处理困难和数据回归困难。文中给出了大质量法、直接激励法和惯性载荷法的动力学方程，指出各种方法的应用条件。计算结果表明，直接激励法简捷实用，优于惯性载荷法和大质量法。     

Spin-axis pointing of a magnetically actuated spacecraft

Attitude regulation proves to be a challenging problem, when magnetic actuators alone are used as attitude effectors, since they do not provide three independent control torque components at each time instant. In this paper a rigorous proof of global exponential stability is derived for a magnetic control law that leads the satellite to a desired spin condition around a principal axis of inertia, pointing the spin axis toward a prescribed direction in the inertial frame. The technique is demonstrated by means of numerical simulation of a few example maneuvers. An extensive Monte Carlo simulation is performed for random initial conditions, in order to investigate the effect of changes in control law gains.     

帆板转动时卫星姿态的非线性控制

当帆板转动时，卫星姿态因系统质量特性的改变和帆板驱动力矩的作用而发生扰动，本文采用一种具有鲁棒性的非线性控制方法，实现了高精度的卫星姿态控制。     

Stability of triangle libration points in generalized restricted circular three-body problem

Equilibrium positions of a small-mass body are considered with respect to a precessing dumbbell. The dumbbell represents two rigidly fixed spherical gravitating bodies. Such a system can be considered as a model of a binary asteroid. Stability of relative equilibrium positions with equal distances from the small mass to the attracting centers is studied. By analogy with the classical restricted three-body problem, these positions are referred to as triangle libration points. It is shown that the character of stability of these libration points is determined by three constant parameters: nutation angle and angular velocity of precession, as well as the ratio of masses at the ends of the dumbbell. Stability conditions are derived in the linear approximation, and the regions of stability and instability in the space of problem parameters are constructed. The paper is a continuation of [1].     

等质量立体五星库仑编队飞行的分析与控制

分析了立体五星编队在静电力和万有引力作用下的静态构型。分别讨论了五星编队在共线和平面情况下的静态构型,着重研究了五星构成立体双直角六棱锥构型时各个卫星所带的静电荷量。由于地球同步轨道的卫星所受到的作用力不仅是万有引力与静电库仑力,还有空气阻力等摄动力,因此只有对其施加控制,卫星才能在静态平衡点保持编队构型的稳定性。本文采用线性二次型最优控制方法来保持编队的静态构型稳定,并通过Matlab实现了五星立体库伦编队飞行控制仿真。     

空间站力矩平衡姿态和动量平衡姿态的研究

研究了空间站的力矩平衡姿态(TEA)及动量平衡姿态(MEA)的求解方法。首先定义了瞬时TEA、平均TEA和MEA的概念并建立了环境力矩在本体系下的数学模型;其次用迭代法确定出瞬时TEA,进一步通过求解非线性方程组计算平均TEA,仿真表明在一个轨道周期中空间站保持在平均TEA时所受外力矩的平均值远小于保持在零姿态的情况;最后提出求解MEA的方法,仿真表明空间站保持在MEA的动量积累及其峰值远小于保持在零姿态的情况。