欠驱动双刚体航天器姿态运动规划的数值方法

带球铰连接的双刚体航天器系统在无外力矩作用时,其姿态运动可通过连接双刚体航天器的铰关节进行控制,这种由控制输入数目少于系统自由度的系统称为欠驱动系统.利用系统相对于总质心的动量矩守恒这一特性研究了欠驱动双刚体航天器的三维姿态运动控制问题.导出带球铰连接的双刚体航天器系统三维姿态运动控制模型,并将系统的控制问题转化为无漂移系统的运动规划问题,利用最优控制技术和小波分析方法.提出基于小波逼近的遗传算法最优运动规划数值算法.通过数值仿真,表明该方法对带球铰连接的欠驱动双刚体航天器三维姿态运动的运动规划是有效的.     

物—伞系统运动稳定性判据

物—伞系统运动稳定性分析是飞行器回收系统设计需深入研讨的重要课题。本文在把伞视作刚体的条件下,按物—伞系统平面运动方程考察其在平衡状态附近的稳定性,给出了运动稳定性判据。这里,伞可以是单伞也可以是双伞。     

利用刚体—质点模型法计算物—伞系统运动轨迹的基本方程

物－伞系统运动轨迹计算是飞行器回收系统设计的重要课题，文中采用刚体－质点模型推导出该问题的求解方程，特别着重讨论了物体运动状态的确定。与通常讨论物体运动将转动参考点取在质心不同，文中针对和的－伞系统的实际，把物体转动的参考点取在物－伞连接点。     

采用系统模态时柔性航天器的混合坐标动力学方程

首先建立了采用任意浮动参考架时的柔性航天器动力学方程,然后选择连体坐标系为浮动参考架,解所得到的动力学方程的特征值问题,得到整个航天器系统的系统模态。通过模态变换,得到用连体系刚体位移和系统模态坐标表示的混合坐标航天器动力学方程。与通常采用部件模态得到的混合坐标动力学方程不同,这时动力学方程中刚体运动和弹性运动已无惯性耦合。同时也和采用系统自由弹性模态不同,这时刚体坐标直接反映航天器刚体运动。论文最后给出了两个算例。     

欧拉动力学方程中的新混沌吸引子及其分析

分析了欧拉动力学方程的非线性特性,包括自由刚体的等能周期运动及受扰刚体的各种周期、准周期和混沌运动;以Newton-Leipnik系统、Lorenz系统族为该系统的特例,得出了与轨道流形理论不同的吸引子存在结论;发现了连续动力学系统的周期、准周期吸引子及一大类新的混沌吸引子;分析了系统的敛散机制和各类吸引子的结构特征。     

双连杆柔性机械臂的动力学仿真

基于柔性杆件的有限段模型，利用Lagrange方程建市了包含刚性支座的双连杆柔性机械臂的刚、柔混合多体系统动力学模型并完成了系统的动力学仿真。仿真结果表明，有限段方法用于处理含柔性杆件的多柔体系统动力学问题是行之有效的，既可在宏观层次上模拟各柔性臂的大范围刚体运动，又可在微观层次上模拟各柔性臂的弹性振动，能够准确地反映此类系统刚柔耦合运动特性。     

双Rodrigues参数方法及其在姿态确定中的应用

提出了一种利用Rodrigues参数序对描述刚体姿态运动的方法。首先证明了刚体的任一     

用Kane方法建立末敏弹减速和稳态扫描段模型

引入多刚体运动模型，详细分析了伞刚体和弹刚体的受力和运动特性，运用Kane方法建立末敏弹在减速运动和稳态扫描段的完整运动模型，并进行数字仿真，仿真结果与实验结果有很好的一致性，并充分显示了该模型在数字仿真中的优越性。     

用Kane方法建立未敏弹减速运动和稳态扫描段模型

K引入多刚体运动模型，仔细地分析了伞刚体和弹刚体的受力和运动弹性，运用Kane方法建立末敏弹在减速运动和稳态扫描段完整的运动模型，并进行数字仿真，仿真结果与实验结果有很好的一致性，并充分显示了该模型在进行数字仿真的优越性。     

系绳力对降落伞拉直过程的影响

文章采用多刚体模型研究了伞绳的系力对降落伞拉直过程的影响。在物伞系统的动力学模型中将引导伞、伞包、伞绳及回收物处理为开链式多刚体,提出了n阶的递推算法来求解绳段间的约束力。利用该模型研究了伞绳的系力对物伞系统运动的影响。仿真结果表明伞绳的系力是影响伞包角加速度的关键因素。     

充液卫星平放式贮箱内液体晃动的等效力学模型

本文研究带平放式贮箱的三轴定向充液卫星的液体晃动及其姿态动力学问题，建立了充液系统的等效力学模型，并由该模型研究了充液卫星的姿态稳定性，得到了主刚体作平面摆动时系统的姿态稳定性判据     

Stability of spinning satellite under axial thrust and internal mass motion

This paper considers a spinning rigid body and a particle with internal motion under axial thrust. This model is helpful for gaining insights into the nutation anomalies that occurred near the end of orbit injections performed by STAR-48 rocket motors. The stability of this system is investigated by means of linearized equations about a uniform spin reference state. In this model, a double root does not necessarily imply instability. The resulting stability condition defines a manifold in the parameter space. A detailed study of this manifold and the parameter space shows that the envelope of the constant solutions is in fact the stability boundary. Only part of the manifold defines a physical system and the range of frequency values that make the system unstable is restricted. Also it turns out that an increase of the spring stiffness, which restrains the internal motion, does not necessarily increase the stability margin. The application of the model is demonstrated using the orbit injection data of ESA's Ulysses satellite in 1990.     

导弹姿态控制系统鲁棒稳定性分析

研究了某型导弹弹体模型及其在飞行中的运动特性，对其姿态控制系统模型进行了简化，分析了导弹姿态控制系统在参数摄动条件下的动态特性，并时影响系统性能的不同参数偏差间的相互补偿进行了研究。结果表明，在某些测试参数偏差超出允许的条件下，如果系统有足够稳定裕度，只要不是功能性问题，仍可以进行发射。     

单通道控制旋转弹系统动力学建模与Hopf分岔

为准确预测旋转弹系统的锥形运动形态并判断其稳定性，提出一对鸭舵引起的气动不对称性以及可能引起复杂非线性动力学特性的非线性因素，建立能准确描述单通道控制旋转弹系统姿态运动的复数形式的动力学模型并分析讨论其动态稳定性条件。利用分岔理论对单通道控制旋转弹系统开展Hopf分岔研究，给出了Hopf分岔发生的判断准则；推导了用于判定极限环稳定的第一Lyapunov系数。数值仿真结果验证了条件的正确性与有效性并发现了拟周期运动及混沌运动。研究结果为旋转弹的控制参数设计及结构参数设计提供理论参考。     

一类挠性航天器的变结构控制

本文研究在控制器能量受限条件下，一类挠性航天器的姿态控制问题。考虑刚性主体上带有挠性梁的航天器，并假定系统在一平面内作旋转运动。针对航天控制工程中执行机构的工作模式，基于系统的无穷维模型，本文设计了简单易行的变结构控制方案，并证明了相应的闭环系统的渐近稳定性。数值仿真和物理实验结果显示了所设计的控制算法的有效性。     

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.     

带柔性伸缩附件航天器几何非线性振动稳定性

研究由中心刚体和可伸缩柔性附件组成的非线性刚柔耦合系统，不同于大多数文献只研究柔性附件的横向弯曲变形对系统动态特性的影响，同时考虑了柔性附件的拉伸变形、截面转角变化同弯曲变形的相互耦合作用，并且以非线性几何关系作为基本出发点，建立了伸缩运动同柔性变形、姿态运动之间的非线性耦合动力学模型，然后基于能量积分和动量矩积分构造首次积分，分析了非线性耦合系统的运动稳定性。     

Periodic motions of a nearly dynamically symmetric satellite in the neighborhood of hyperboloidal precession

The motion of a satellite close to a dynamically symmetric solid body in a Newtonian gravitational field over a circular orbit is studied. The system of differential equations describing the body’s motion is close to a system with cyclic coordinate. New classes of periodic motions are constructed in the neighborhood of a known partial solution to an unperturbed problem, hyperboloidal precession of a dynamically symmetric satellite. In the resonance case, when the ratio of one frequency of small oscillations of a reduced system with two degrees of freedom in the neighborhood of a stable equilibrium position to the frequency of cyclic coordinate variation is close to an integer number, there exist one or three families of periodic motions that are analytic in terms of fractional powers of a small parameter. A study of stability of these motions was performed with the help of KAM (Kolmogorov-Arnold-Moser) theoty. Faling the described resonance there exists a unique family of periodic motions that is analytic in terms of integer powers of a small parameter. The check-up of stability of these motrons was carried out. We distinguished the cases of parametric resonance, resonances of the third and fourth orders, and a non-resonant case. In the resonance cases our study relies on well-known results on stability of Hamiltonian systems during resonances [1]. In the non-resonant case we use the KAM theory [2].     

Evolution of Motion of a Binary Planet

A model of a binary planet, consisting of a material point of small mass and a deformable viscoelastic sphere, is suggested. The center of mass of the binary planet moves in the gravitational field of a central body in the plane, which contains planets forming the binary planet. A deformable spherical planet rotates around the axis orthogonal to the plane of planetary motion. Planet deformations are described by the linear theory of viscoelasticity. It is shown that with an appropriate approximation of the gravitational potential, there is a class of quasicircular orbits, when the eccentricities of an orbit of the center of mass of a binary planet and an orbit, describing mutual planet motion, are equal to zero. The further evolution of motion is investigated in this class of orbits with the use of the canonical Poincare–Andoyer variables. Corresponding averaged equations are found, and phase pictures are constructed; the stability of stationary solutions is investigated on the basis of equations in variations. For the Solar system planets with their satellites, forming binary planets, the application of the presented model allows us to conclude that satellites sooner or later will fall on the corresponding planets.     

On the stability of spinning satellites

We study the directional stability of rigid and deformable spinning satellites in terms of two attitude angles. The linearized attitude motion of a free system about an assumed uniform-spin reference solution leads to a generic MGK system when the satellite is rigid or deformable. In terms of Lyapunov’s stability theory, we investigate the stability with respect to a subset of the variables. For a rigid body, the MGK system is 6-dimensional, i.e., 3 rotational and 3 translational variables. When flexible parts are present the system can have any arbitrary dimension. The 2×2 McIntyre–Myiagi stability matrix gives sufficient conditions for the attitude stability. A further development of this method has led to the Equivalent Rigid Body method. We propose an alternative practical method to establish sufficiency conditions for directional stability by using the Frobenius–Schur reduction formula. As practical applications we discuss a spinning satellite augmented with a spring–mass system and a rigid body appended with two cables and tip masses. In practice, the attitude stability must also be investigated when the spinning satellite is subject to a constant axial thrust. The generic format becomes MGKN as the thrust is a follower force. For a perfectly aligned thrust along the spin axis, Lyapunov’s indirect method remains valid also when deformable parts are present. We illustrate this case with an apogee motor burn in the presence of slag. When the thrust is not on the spin axis or not pointing parallel to the spin axis, the uniform-spin reference motion does not exist and none of the previous methods is applicable. In this case, the linearization may be performed about the initial state. Even when the linearized system has bounded solutions, the non-linear system can be unstable in general. We illustrate this situation by an instability that actually happened in-flight during a station-keeping maneuver of ESA’s GEOS-I satellite in 1979.