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.     

Satellite dynamics under the influence of gravitational and aerodynamic torques. A study of stability of equilibrium positions

The dynamics of the rotational motion of a satellite, moving in the central Newtonian force field under the influence of gravitational and aerodynamic torques, is investigated. The paper proposes a method for determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of aerodynamic torque and the major central moments of inertia; the sufficient conditions for their existence are obtained. For each equilibrium orientation the sufficient stability conditions are obtained using the generalized energy integral as the Lyapunov function. The detailed numerical analysis of the regions where the stability conditions of the equilibrium positions are satisfied is carried out depending on four dimensionless parameters of the problem. It is shown that, in the general case, the number of satellite’s equilibrium positions, for which the sufficient stability conditions are satisfied, varies from 4 to 2 with an increase in the value of the aerodynamic torque magnitude.     

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.     

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.     

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.     

卫星双向时间频率传递中的Sagnac效应

 结合卫星双向时间频率传递技术,提出了在卫星运动情况下Sagnac效应解决方案。卫星双向时间频率传递技术是基于地球同步卫星进行的。地球同步卫星在各种摄动力的影响下,相对于地面上的某点不是绝对静止的,而是作小幅度日周期性运动。 Sagnac 效应与卫星和地面观测站的位置密切相关,卫星的运动直接导致了 Sagnac 效应也具有日周期变化的特征。使用高精度实测卫星轨道数据对 Sagnac 效应进行计算分析,结果表明：由卫星运动引起的Sagnac效应值具有与卫星运动一致的周日变化规律特征,大小达到几百皮秒的量级,与传统的将同步卫星作为静止点处理相比,提高了Sagnac效应误差的修正精度。该方案对于各种高精度卫星时间比对技术和卫星导航等领域具有重要的应用价值。     

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.     

卫星垂直方向充退磁线圈设计新方法

文章提出采用电连接器对接安装方式设计卫星垂直方向充退磁线圈设备,可使卫星磁试验过程中去除吊装作业,大大提高其安全性。根据该思路进行线圈组位置布局及电性能参数的分析设计,然后完成充退磁线圈设备的结构设计和静力学有限元分析。在北京卫星环境工程研究所的CM2试验室内,研制完成的充退磁线圈设备已经在多颗卫星磁试验中获得很好地应用,它具有制造工艺简单、节省材料、操作安全方便等特点。     

Motion of a satellite equipped with a pitch flywheel and magnetic coils in gravitational field

A satellite equipped with a magnetic attitude control system and a pitch flywheel has been considered. The system performance in the transient mode has been investigated. The characteristic exponent of the system have been approximated for a satellite on a circumpolar orbit. In the steady-state mode of gravitational attitude, small motions are considered in the vicinity of equilibrium. The attitude accuracy has been analyzed. The algorithm of an arbitrary but given attitude of the satellite in the orbital plane has been investigated. A numerical simulation has been performed.     

太阳,地球,卫星相关模拟源设计

“风云二号”自旋稳定地球同步气象卫星，以地球脉冲作为姿态控制基准，以太阳脉冲作为图像扫描基准，太阳、地球、卫星三者之间的相对关系在连续不断地运动变化。为了验证扫描成像原理和在地面测试卫星的成像质量，需对三者的相对关系进行研究。在此基础上，研制出太阳、地球、卫星相关模拟源，成功地用电子信号准确模拟“风云二号”卫星在静止轨道上感受到的不断变化的太阳、地球信号，使卫星的成像测试顺利进行，同时发现了卫星设计中存在的问题。     

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。     

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.     

大型高轨通信平台主动段热变形分析

对于大型高轨通信卫星等的高价值卫星,为增强卫星的抗风险能力,对极端温度环境条件和相较一般发射工作程序有所偏离的情况下,进行了卫星平台的热分布情况分析。采用了能够较全面深入反映平台结构热变形的3D舱板模型的有限元分析方法。表明最高温度50.8 ℃,最低温度-11.89 ℃,未超出卫星的极限温度要求,卫星平台的热性能有一定保持能力。舱板厚度方向温差2.5 ℃。对分析的热分布结果与一般条件下的热平衡试验结果进行了分析比较,分析结果较一般条件下的热平衡试验结果温度高出约25 ℃。在热分析结果基础上所做的卫星平台热变形分析,表明舱板的最大变形在抛罩时刻为0.185 mm,在星箭分离时刻为0.506 mm,已经接近结构局部精度的要求量级。在抛罩和星箭分离时的服务舱仪器板的热变形方向相反,预示着这里是热振动的潜在振源。     

小卫星太阳电池阵结构声振响应分析研究

针对高频段太阳电池阵结构声振问题求解中的结构模态参数不确定性,文章从统计模态和能量平衡的角度出发,深入研究了复合材料面板太阳电池阵夹层结构的统计能量分析参数确定及功率流模型创建方法,并快速得到了太阳电池夹层结构的声振响应。对比分析与试验结果,发现二者吻合很好,因而验证了该声振响应分析方法用于小卫星太阳电池阵结构的有效性,并可作为小卫星工程研制中太阳电池阵结构动力学分析的有益补充。     

在轨地球同步卫星地球敏感器干扰及指向计算

从工程应用角度,基于太阳、月球位置和卫星轨道根数推导了太阳和月球对地球同步轨道卫星红外地球敏感器干扰的计算公式及预报方法,同时给出了安全模式下卫星Z轴跟踪太阳时星上天线指向变化的计算模型。计算结果和卫星下传遥测数据验证了方法的正确性,可用于实际卫星管理。     

TETHERED SATELLITE SYSTEM ANALYSIS (1) — TWO-DIMENSIONAL CASE AND REGULAR DYNAMICS

The study on tethered satellite system (TSS) in two-dimensional in-planar motion is restricted in that the tether is assumed to be massless. The equations of motion are given in a spherical coordinate system to describe the magnitude (tether length) and direction angle of the position vector between the satellites. A length rate control algorithm is adopted, and the controlled motion of the directional angle by the algorithm will have a stable equilibrium state. The equilibrium state is a fixed point if the orbit of the base-satellite is circular, and a limit cycle if the orbit is elliptic. The value and stability of the equilibrium state are determined by the parameters of the control algorithm, and the bifurcation analysis is also given. Two typical TSS missions have been simulated.     

Stability and chaos of a damped satellite partially filled with liquid

The stability and chaotic motions of a damped satellite partially filled with liquid which is subjected to external disturbance are investigated in this paper. With linearization analysis, the stability of the two non-trivial equilibrium points is studied. The homoclinic and heteroclinic orbits are found by using the undetermined coefficient method, and the convergence of the series expansions of these two types of orbits is proved. It analytically demonstrates that there exist homoclinic orbits of the Si’lnikov type that join the two non-trivial equilibrium points to themselves, and therefore smale horseshoes and the horseshoe chaos occur for this system via the Si’lnikov criterion. In addition, there also exists a heteroclinic orbit connecting the two non-trivial equilibrium points. Numerical simulations are also given, which verify the analytical results. The system can be chaotic through period-doubling bifurcations as the amplitude of the external disturbance varies, and backward period-doubling bifurcations as the angular momentum of the rotor varies.     

Stability and chaos of a damped satellite partially filled with liquid

The stability and chaotic motions of a damped satellite partially filled with liquid which is subjected to external disturbance are investigated in this paper. With linearization analysis, the stability of the two non-trivial equilibrium points is studied. The homoclinic and heteroclinic orbits are found by using the undetermined coefficient method, and the convergence of the series expansions of these two types of orbits is proved. It analytically demonstrates that there exist homoclinic orbits of the Si’lnikov type that join the two non-trivial equilibrium points to themselves, and therefore smale horseshoes and the horseshoe chaos occur for this system via the Si’lnikov criterion. In addition, there also exists a heteroclinic orbit connecting the two non-trivial equilibrium points. Numerical simulations are also given, which verify the analytical results. The system can be chaotic through period-doubling bifurcations as the amplitude of the external disturbance varies, and backward period-doubling bifurcations as the angular momentum of the rotor varies.     

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].     

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。