Artificial satellites orbits in 2:1 resonance: GPS constellation

In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J₂₀ and J₄₀ and the tesseral harmonics J₂₂ and J₄₂. Through an averaging procedure and successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, three critical angles are studied. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. Through the resonance overlap criterion the possible regular and irregular motions are investigated by the time behavior of the semi-major axis, argument of perigee and eccentricity. The largest Lyapunov exponent is used as tool to verify the chaotic motion.     

Artificial satellites orbits in 2:1 resonance: GPS constellation

In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J₂₀ and J₄₀ and the tesseral harmonics J₂₂ and J₄₂. Through an averaging procedure and successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, three critical angles are studied. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. Through the resonance overlap criterion the possible regular and irregular motions are investigated by the time behavior of the semi-major axis, argument of perigee and eccentricity. The largest Lyapunov exponent is used as tool to verify the chaotic motion.     

Dynamics and chaos control of asymmetric gyrostat satellites

The motion of a free gyrostat consisting of a platform with a triaxial ellipsoid of inertia and a rotor with a slight asymmetry with respect to the axis of rotation is considered. Dimensionless equations of motion for a system with perturbations caused by the small asymmetries of the rotor are written in Andoyer-Deprit variables. These perturbations result in a chaotic layer in the separatrix vicinity. Heteroclinic and homoclinic trajectories are written in analytical form for gyrostats with different ratios of their moments of inertia. These trajectories are used to construct a modified Melnikov function, and to produce control that eliminates separatrix chaos. The Poincare sections and Melnikov function are constructed via numerical modeling that demonstrates the effectiveness of control.     

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].     

非线性飞行混沌运动的修正RBF神经网络控制

如何求神经网络控制使非线性空间飞行混沌运动不会发生。该法是在输出层用回归权代替常数权再用EM算法来估计回归权的参数 ,这样修正的RBF的神经网络控制就可使非线性空间飞行不会出现混沌现象。这种算法R Langari,L Wang&J Yen (1997) [1] 在研究径向基函数网络时提出过。其突出的优点是把复杂的多参数的最优化问题分离为N个小型最优化问题 ,这里N是隐藏层单元数。     

用反馈法主动控制Duffing混沌系统的仿真研究

采取工程中常用的反馈法 ,结合主动隔振的控制原理 ,对Duffing振子混沌振动进行了主动隔振仿真研究 ,取得了较好的隔振效果。研究结果表明了在混沌振动系统中应用主动隔振技术的有效性。     

一类不确定混沌系统的强鲁棒跟踪控制

基于指数终端吸引子的有限时间快速收敛特性,将指数型快速终端滑模引入一类不确定混沌系统,提出了一种新的滑模变结构跟踪控制。证明了系统跟踪误差变量在有限时间内能以较快的收敛速度到达各级滑模面的邻域,并最终收敛至平衡点附近很小的区域,系统有良好的动态性能。Dulling系统仿真结果表明该控制策略有强鲁棒性。     

Chaotic oscillations of spacecraft with an elastic radially oriented tether

A mechanical system consisting of a spacecraft with weightless elastic tether and load is considered in the paper. The spacecraft motion under the action of tensile force of a radially oriented tether is investigated. It is shown that elastic tether oscillations can result in appearance of chaotic modes of spacecraft motion. By means of the Melnikov method a condition is obtained, allowing one to determine the measure of damping sufficient for prevention of these chaotic modes. The influence of system’s mass-geometric and elastic characteristics on the form of phase portrait and on the value of periodic disturbance, caused by oscillations of the elastic vertical tether, is studied.     

地月低能轨道转移的混沌控制方法

针对航天器在混沌区域的滑行时间过长，提出一种低能地月轨道转移的混沌控制方法。首先通过地月圆形限制性三体问题(CRTBP)的庞加莱截面图，将混沌区域进行分层并分析其规律，再利用混沌轨道对初始状态高度敏感的特性，在尽可能减少运送时间的前提下实现地月低能轨道转移。该方法的优点是利用混沌区域的固有规律，不需要依靠周期轨道特性。仿真结果表明，本文提出方法仅需施加2~4次脉冲，明显缩短混沌区域的滑行时间，从而实现地月低能转移。     

高精度低连接刚度大惯量扫描镜控制系统设计

针对三轴稳定卫星内低连接刚度条件下的大惯量扫描镜负载在低速摆动时易出现机械谐振的问题,基于电流-速度-位置三闭环控制结构,研究并提出一种有效的易于工程实现的优化控制方法,抑制机械谐振同时提高扫描镜系统的控制性能.首先,根据动力学关系对低刚度连接的电机与扫描镜控制对象建立理论的简化控制模型.然后,分析加速度反馈抑制谐振、...     

Three-frequency resonances in the problem of fast rotation of an asymmetric body in elliptical orbit

The paper presents a classification of resonance problems generated by the highest-degree term of the perturbing function in the problem of fast rotation of an asymmetric solid body in elliptic orbit in a central gravitational field. Explicit formulas are obtained for Hamiltonians of all Hamiltonian systems that deter-mine motions in the neighborhood of resonances. Basic resonance effects are described.     

用三轴气浮台进行混沌控制与反控制研究

以航天器姿态运动为工程背景，以三轴气浮台为物理实验平台，研究了混沌控制与反控制问题；提出了用外控制力矩进行混沌化，然后再将混沌控制信号施加于动量轮来进行混沌控制实验的方法；通过引入非线性解耦反馈，构造了一种易于物理实现的具有更强代表性的连续非线性系统，从中发现了一大类新的形态各异的混沌吸引子。     

航天器共振轨道研究

建立航天器非开普勒运动理论是航天技术发展的必然。提出了一类非开普勒轨道——共振轨 道。共振是自然界的一种普遍现象,当发生共振时,很小的输入可以使系统的状态产生较大 变化。研究表明航天器在推力作用下的非开普勒运动在参数平面内可以视为一种受迫振 动,也会发生共振现象。因此,可以利用共振原理来研究航天器的运动,称这样一类非开普 勒轨道为共振轨道。首先通过合理地选择轨道描述参数、时间尺度和推力描述方式建立 航天器共振轨道的动力学模型。然后讨论航天器在推力作用下轨道运动的振动规律,并给出 共振轨道的概念及轨道方程。最后提出基于共振轨道的机动轨道设计方法。
     

Chaos and its avoidance in spinup dynamics of an axial dual-spin spacecraft

Attitude dynamics of a dual-spin spacecraft (DSSC) and a torque-free angular motion of a coaxial bodies system are considered. Some regimes of the heteroclinic chaos are described. The local chaotization of the DSSC is investigated at the presence of polyharmonic perturbations and small nutation restoring/overturning torques on the base of the Melnikov method and Poincaré Maps. Reasons of the chaotic regimes initiation at the spinup maneuver realization are studied. An approach for the local heteroclinic chaos escape/avoidance at the modification of the classical spinup maneuver is suggested.     

Theory of physical libration of the Moon with the liquid core: Forced librations

For a two-layer model of the Moon that consists of a solid nonspherical mantle and an ellipsoidal homogeneous liquid core, a theory of forced librations under the effect of gravitational Earth’s moments has been developed. The motion of the Moon over its orbit has been described by the high-accuracy theory of DE/LE-4 orbital motion. Tables have been constructed that present forced librations of the Moon caused by the second harmonic of its force function, in the neighborhood of its motion according to the generalized Cassini laws. Disturbances of the first-order with respect to dynamic compressions of the Moon and its core are obtained in analytical form for Andoyer variables and Poincare variables and for the projection of the angular velocity vector of Moon’s mantle rotation and the Poincare coordinate system (relative to which core’s liquid accomplishes simple motion) on its major central axes of inertia, as well as for the classical variables in the Moon libration theory, etc. Constructed tables of the forced librations theory give the amplitudes and periods of librations and combinations of arguments of the orbital motion theory that correspond to libration parameters. The interpretation of basic variations has been given and a comparison with the previous theories has been carried out, in particular with the modern empirical theory constructed based on the laser observation data.     

A Study of Oscillations near a Resonance during the Descent of a Spacecraft in the Atmosphere

An analysis of the stability of the resonance motion of a spacecraft with a small asymmetry during its descent in the atmosphere is carried out. In the vicinity of the main resonance, the action–angle variables are introduced and an equation of the variation of action is composed. A conclusion related to the stability of the resonance motion is made from the investigation of this equation. Sufficient conditions of stability of the resonance motion of a spacecraft are obtained and represented in a form convenient for analysis.     

Recent Advances in the Theoretical and Applied Study on Compressible Turbulent Flow over Aerospace Vehicles

This paper focused on the fundamental and applied research of turbulent flows encountered in the hypersonic flight of aerospace vehicles,which take place in the boundary layer and mixing layer.As to the plate boundary layer,LES approach has been used to simulate the flows over compression corners and incident shock waves,revealing that turbulent flows would significantly inhibit the boundary layer separation caused by shock wave-boundary layer interaction(SWBLI).The boundary layer transition over a circular cone has been analyzed through stability analysis and wind-tunnel test,by which the angle-of-attack effect in case of small angle of attack has been studied.Non-linear evolution process and secondary instability structure in the supersonic mixing layer(Mc=0.5) were initially figured out through the study of mixing layer,and knowledge of the flow control mechanism of the boundary layer and mixing enhancement mechanism of the mixing layer has been obtained through this research.Artificial boundary-layer transition technique based on subharmonic resonance has been proposed and applied to the flow control in a scramjet inlet,inhibiting the flow separation of the boundary layer while improving the inlet performance.To guarantee the mixing of kerosene and supersonic airflow in the scramjet combustor,the mixing enhancement method based on subharmonic resonance has been adopted and a concept of combustor with smooth wall and low internal drag has been proposed for ignition and stable combustion.Finally,future turbulence research and technological development of aerospace vehicles is predicted.     

限制性四体问题中的时间相关不变流形

借助有限时间Lyapunov指数（FTLE）定义了拉格朗日拟序结构（LCS）,并将LCS作为不变流形的替代物。针对日-地-月双圆模型（BCM）,利用LCS研究了限制性四体问题（R4BP）中的时间相关不变流形（TDIM）的性质。采用数值方法验证了TDIM是运动分界面和轨道不变集。继而,利用二分法对给定Poincare截面上的LCS进行了精确提取,通过一系列等能量面上的LCS描绘出TDIM在给定截面上的构形。最后,借助TDIM,初步研究了低能奔月轨道在非自治系统BCM中的直接构建。     

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。