高阶带谐摄动下卫星相对运动精确动力学模型

在考虑J 2 项摄动的卫星相对运动精确动力学模型基础上,推导了可以精确到任意阶带谐非球形引力摄动的卫星相对运动精确动力学模型,还给出了一组简洁的基于参考卫星轨道要素（Reference Satellite Variables）的微分方程,能够描述精确到任意阶带谐非球形引力的卫星地球轨道运动。由于在模型推导过程中没有引入任何简化,新推导的结果适用于任意偏心率的地球轨道。     

地球轨道卫星电推进变轨控制方法

针对地球同步轨道（GEO）卫星,采用电推进系统完成转移轨道变轨。采用基于Lyapunov函数的反馈控制方法确定时间最短变轨策略。首先在开普勒模型下研究变轨过程,然后在开普勒模型的基础上考虑地球J2项摄动和地球阴影,最后在全引力模型下研究变轨过程,即在开普勒模型的基础上考虑地球非球形引力摄动、日月第三体引力摄动、太阳光压摄动和地球阴影。仿真结果显示在变轨过程中摄动项不可忽略,除地球J2项摄动外还应该考虑日月第三体引力摄动和太阳光压摄动。对比上述三组仿真结果,发现考虑摄动后轨道转移时间的增加比燃料消耗的增加更为明显。数值仿真结果表明本文研究对未来的全电推进任务具有良好的通用性和应用参考价值。     

摄动椭圆参考轨道的相对运动状态转移方程

当面质比不同的主从卫星在近地轨道上作编队飞行时,大气阻力摄动和J2项摄动就成为影响编队队形的两个最主要的因素,这样描述相对运动的状态转移方程必须考虑这两项摄动。该文利用相对轨道要素法推导了包含J2项摄动和大气阻力摄动参考轨道为椭圆的卫星编队相对运动较精确的状态转移方程。当主从卫星的面质比相等时大气阻力摄动对卫星编队队形的影响很小而可以忽略,这样上面的状态转移方程可以化为更简单的形式。仿真结果表明该状态转移方程能较精确的预测编队飞行的相对运动。     

基于受摄轨道模型的小卫星轨道摄动分析研究

小卫星在实际运行中受到多种摄动力的作用,这会对其轨道造成不同程度的影响,因此在小卫星的轨道设计与控制中,摄动是必须考虑的重要因素。本文以500km高的小卫星太阳同步轨道为研究对象,运用轨道摄动的基本理论,估计了地球非球形引力、大气阻力、太阳光压及第三体引力的量级并进行比较;建立小卫星轨道摄动分析模型,并在此模型的基础上,利用计算机仿真技术,对小卫星轨道摄动问题展开仿真研究,验证了几种主要摄动力的量级估计的结果,分析比较了几种主要摄动力对小卫星运行轨道的影响程度及规律,本文结果对小卫星轨道设计与控制具有很好的参考价值。     

摄动条件下椭圆轨道卫星相对运动研究

基于严格定义的相对轨道要素,考虑非球形引力、大气阻力和三体引力等摄动力的影响,用拟平均根数法添加相关摄动项,推导了椭圆轨道摄动条件下无奇点的卫星近距离相对运动模型。分析了考虑摄动力的影响时相对轨道要素的特性,并据此分析了各摄动力对卫星相对运动轨道预报精度的影响,比较了有无摄动的相对运动模型与精确解间的误差。算例验证了方法与结果的正确性和有效性。研究结果完善了相对轨道要素的基本理论,并将其适用范围拓展至摄动条件下的椭圆基准轨道卫星相对运动研究领域。     

分布式卫星轨道构形的大气摄动分析及修正方法

在低轨道运行的分布式卫星受大气摄动的影响,其轨道构形很快遭到破坏,环绕卫星的相对运动轨迹中心不断发生漂移。本研究的目的在于建立一种降低大气摄动对分布式卫星轨道构形影响的补偿方法,以使分布式卫星的轨道构形能够更好地自然维持。研究基于考虑高度变化和太阳周日变化的大气密度模型,得出分布式卫星不同初始相位环绕卫星的长半轴摄动方程。并提出一种补偿大气摄动影响的长半轴修正方法。仿真结果显示,采用此大气摄动补偿方法能够在给定时间内大大降低大气摄动的影响,从而显著提高分布式卫星轨道构形的自然维持能力。     

大气阻力摄动对卫星编队飞行队形的影响分析

为了分析大气阻力摄动对卫星编队队形的影响,利用相对轨道根数法推导了包含大气阻力摄动的卫星编队相对运动的状态转移方程。仿真结果表明当几何形状和质量不同的两颗卫星在低轨道做编队飞行时,大气阻力摄动对编队队形的影响很大而不能忽略;当主卫星的半长轴相等时,主卫星轨道的偏心率越大编队飞行受大气阻力摄动的影响也越大;大气阻力摄动主要影响编队飞行迹向相对距离。     

基于轨道摄动解的卫星编队飞行

用完全不同的方法推导出一种两颗卫星相对运动的表达式.首先,它描述的是一颗真实的卫星相对一颗在理想轨道上运动的虚拟卫星的运动,而这正是研究编队飞行所必须的;其次,这个表达式将真实卫星相对虚拟卫星的三维位置表示成虚拟卫星的Brouwer平根数及两卫星轨道根数之差的函数.据此便可以充分应用已有的关于轨道摄动的研究成果.作为一个基本模型,首先讨论了一颗真实卫星相对虚拟卫星形成椭圆型地面轨迹的飞行方式.基于轨道长期摄动的已有结果可以很容易地揭示这种飞行方式的长期变化,从而可以毫无困难地制定出轨道调整的策略.最后还研究了三颗卫星以同一条椭圆轨迹飞行的轨道设计和控制问题,该椭圆以虚拟卫星为中心.     

卫星轨道摄动频谱分析

本文基于Ｌｉｅ级数的方法对卫星轨道摄动进行了频谱分析。这种摄动是由地球引力场的所有带谱调和项和田谐调和项引起的。为了适用小偏心率轨道，采用了Ｈｉｌｌ变量来描述卫星轨道，并在所获得的谱分析式中保留了所有与偏心率ｅ无关的项。在这个基础上又经过简单的变换给出了卫星位置摄动三分量的谱分析式。     

地球卫星动力学定轨中摄动模型的选取

地球卫星动力学定轨中需要依据卫星轨道高度考虑不同的摄动项,以提高定轨精度。针对这一需求,分析了不同轨道高度下卫星所受的地球非球形、日月引力、太阳光压和大气阻力4种摄动项对二体模型的校正量,数值仿真表明实验结果与摄动项的力学分析相吻合,另外,给出了地球卫星动力学定轨中不同轨道下卫星摄动项的选取原则。     

Determination of attitude motion of the <Emphasis Type="Italic">Foton M-3</Emphasis> satellite according to the data of onboard measurements of the Earth’s magnetic field

The results of reconstruction of rotational motion of the Foton M-3 satellite during its uncontrolled flight in September 2007 are presented. The reconstruction was performed by processing the data of onboard measurements of the Earth’s magnetic field obtained by the DIMAC instruments. The measurements were carried out continuously throughout the flight, but the processing technique dealt with the data portions covering time intervals of a few orbital revolutions. The data obtained on each such interval were processed jointly by the least squares method with using integration of the equations of satellite motion relative to its center of mass. When processing, the initial conditions of motion and the used mathematical model’s parameters were estimated. The results of processing 16 data sets gave us complete information about the satellite motion. This motion, which began at a low angular velocity, had gradually accelerated and in five days became close to the regular Euler precession of an axisymmetric solid body. At the end of uncontrolled flight the angular velocity of the satellite relative to its lengthwise axis was 0.5 deg/s; the angular velocity projection onto the plane perpendicular to this axis had a magnitude of about 0.18 deg/s.     

编队卫星相对运动描述方法综述

对于近地轨道卫星编队飞行的相对运动理论研究,可以采用的方法包括直角坐标法和 轨道要素法。利用直角坐标法得到的相对运动动力学方程可以用于编队队形控制研究,轨道 要素法能够给出相对运动的运动学描述,便于定量研究摄动影响和进行编队队形设计。分析 了直角坐标法在描述卫星长期编队飞行方面的局限性,综述了利用轨道要素描述编队卫星相 对运动的各种研究方法,包括轨道要素差法、相对轨道要素法和参照轨道要素法等。     

非质心特征点相对位置和姿态估计方法研究

卫星编队飞行中,从星星体上偏离质心的任意特征点,其相对位置和相对姿态运动耦合。本文针对任意点的相对状态估计问题,推导了耦合相对轨道动力学方程和无陀螺相对姿态动力学方程,并且基于PSD敏感器对主星上点光源的视线测量值,提出了基于特征点耦合动力学和质心传统动力学的两种相对状态估计策略。针对每种策略分别设计了EKF和UKF两种滤波算法对相对状态进行估计。最后通过数学仿真对算法的有效性进行了验证,并对其计算量进行了分析。结果表明,四种算法均能对特征点的相对状态进行较高精度的估计。     

Optimal control of a spinning double-pyramid Earth-pointing tethered formation

The dynamics and control of a tethered satellite formation for Earth-pointing observation missions is considered. For most practical applications in Earth orbit, a tether formation must be spinning in order to maintain tension in the tethers. It is possible to obtain periodic spinning solutions for a triangular formation whose initial conditions are close to the orbit normal. However, these solutions contain significant deviations of the satellites on a sphere relative to the desired Earth-pointing configuration. To maintain a plane of satellites spinning normal to the orbit plane, it is necessary to utilize “anchors”. Such a configuration resembles a double-pyramid. In this paper, control of a double-pyramid tethered formation is studied. The equations of motion are derived in a floating orbital coordinate system for the general case of an elliptic reference orbit. The motion of the satellites is derived assuming inelastic tethers that can vary in length in a controlled manner. Cartesian coordinates in a rotating reference frame attached to the desired spin frame provide a simple means of expressing the equations of motion, together with a set of constraint equations for the tether tensions. Periodic optimal control theory is applied to the system to determine sets of controlled periodic trajectories by varying the lengths of all interconnecting tethers (nine in total), as well as retrieval and simple reconfiguration trajectories. A modal analysis of the system is also performed using a lumped mass representation of the tethers.     

Generalized restricted circular three-body problem as a model for dynamics of binary asteroids

Exploration of the Solar System has recently revealed the existence of a large number of asteroids with satellites, which has stimulated interest in studying the dynamics of such systems. This paper is dedicated to the analysis of the relative motion of a binary asteroid. The conditions of existence of such a system (i.e., when its components do not run away) are derived in the Introduction. Then it is assumed that the satellite has no significant effect on the motion of the main asteroid, the latter being modeled as a dumbbell-like precessing solid body. The equations of motion of this system are a two-parameter generalization of the corresponding equations of the restricted circular three-body problem. It is demonstrated that in the system under consideration there exist steady-state motions in which the small asteroid is equidistant from attracting centers at the ends of the dumbbell (an analog to triangle libration points). The conditions of existence of such motions are derived, and the positions with respect to the dumbbell are analyzed in detail. Examination of the stability of the triangle libration points is reduced to investigation of a characteristic equation of the sixth degree. The stability conditions are derived in the case when the main asteroid executes near-planar motion.     

Rotational motion of <Emphasis Type="Italic">Foton M-4</Emphasis>

The actual controlled rotational motion of the Foton M-4 satellite is reconstructed for the mode of single-axis solar orientation. The reconstruction was carried out using data of onboard measurements of vectors of angular velocity and the strength of the Earth’s magnetic field. The reconstruction method is based on the reconstruction of the kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected at a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are substituted in kinematic differential equations for a quaternion that defines the transition from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the satellite rotational motion. A solution of these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of the Earth’s magnetic field and its calculated values. The described method makes it possible to reconstruct the actual rotational satellite motion using one solution of kinematic equations over time intervals longer than 10 h. The found reconstructions have been used to calculate the residual microaccelerations.     

卫星编队飞行的地球扁率摄动分析

本文研究了地球扁率J2项摄动对卫星编队飞行的影响。首先，给出了编队飞行数学描述，推导了轨道根数和相对运动状态的关系式；然后，将卫星编队的受摄影响分解为整体摄动和相对摄动，分别得到了解析解，重点分析了相对摄动规律。研究结果对卫星编队的设计有一定的参考价值。     

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.