Theory and experiment of space electrodynamic tether systems

本文关注在轨航天器中具有导电性能的电动力绳系统,因其复杂动响应特征及潜在应用前景值得学者们深入研究.论文阐述了电动力绳系统的工作原理,对系统的力学建模、动力学行为、控制、应用、在轨实验及地面实验方法等研究进展进行了详细总结,同时提出电动力绳系统有待进一步探究的科学与技术问题.     

空间电动力绳系统理论及实验研究

本文关注在轨航天器中具有导电性能的电动力绳系统,因其复杂动响应特征及潜在应用前景值得学者们深入研究。论文阐述了电动力绳系统的工作原理,对系统的力学建模、动力学行为、控制、应用、在轨实验及地面实验方法等研究进展进行了详细总结,同时提出电动力绳系统有待进一步探究的科学与技术问题。     

Dynamic analysis of a tethered satellite system for space debris capture

Herein we analyze the dynamic behavior of a tethered satellite system for space debris capture, considering the large deformation of a tether. The tethered satellite system is modeled as two point masses and a string, and the equations of motion of the tethered satellite system are derived by using the absolute nodal coordinate formulation. To calculate the net velocity after debris capture, equations are established describing the momentum exchange between the net and the space debris. By using this model, the dynamic responses of the tethered satellite system after debris capture are calculated for the variations of the capture angles and capture velocities of the debris. This allows analysis of the orbital response of the tethered satellite system and the large tensions arising from tether tumbling. Finally, we analyze the effects of varying system parameters of the tethered satellite system and the space debris upon the dynamic responses.     

Quasi-momentum theorem in Riemann-Cartan space

The geometric formulation of motion of the first-order linear homogenous scleronomous nonholonomic system subjected to active forces is studied with the nonholonomic mapping theory. The quasi-Newton law, the quasi-momentum theorem, and the second kind Lagrange equation of dynamical systems are obtained in the Riemann-Cartan configuration spaces. By the nonholonomic mapping, a Euclidean configuration space or a Riemann configuration space of a dynamical system can be mapped into a Riemann-Cartan configuration space with torsion. The differential equations of motion of the dynamical system can be obtained in its Riemann-Cartan configuration space by the quasi-Newton law or the quasi-momentum theorem. For a constrained system, the differential equations of motion in its Riemann-Cartan configuration space may be simpler than the equations in its Euclidean configuration space or its Riemann configuration space. Therefore, the nonholonomic mapping theory can solve some constrained problems, which are difficult to be solved by the traditional analytical mechanics method. Three examples are given to illustrate the effectiveness of the method.     

Review of deployment technology for tethered satellite systems

Tethered satellite systems (TSSs) have attracted significant attention due to their potential and valuable applications for scientific research. With the development of various launched on-orbit missions, the deployment of tethers is considered a crucial technology for operation of a TSS. Both past orbiting experiments and numerical results have shown that oscillations of the deployed tether due to the Coriolis force and environmental perturbations are inevitable and that the impact between the space tether and end-body at the end of the deployment process leads to complicated nonlinear phenomena. Hence, a set of suitable control methods plays a fundamental role in tether deployment. This review article summarizes previous work on aspects of the dynamics, control, and ground-based experiments of tether deployment. The relevant basic principles, analytical expressions, simulation cases, and experimental results are presented as well.     

空间机械臂捕获卫星过程的碰撞动力学模拟及镇定运动的鲁棒控制

讨论了漂浮基空间机械臂捕获未知运动目标卫星的接触碰撞动力学建模和接触碰撞后系统镇定运动的控制问题。利用第二类拉格朗日方法和牛顿-欧拉法分别建立了接触碰撞前漂浮基空间机械臂和目标卫星两分体系统的动力学模型;以此为基础借助于空间机械臂与目标卫星接触点间的运动几何关系、力传递关系,计算了接触碰撞所产生的影响效应;捕获卫星后,联立空间机械臂与卫星接触碰撞前的动力学模型,建立了接触碰撞后两系统组合体动力学模型;并设计了增广鲁棒控制算法,以对受碰撞冲击后处于不稳定的组合体系统进行镇定运动控制。上述控制方法能应用于空间机械臂载体位置不受控情况,并能使组合体系统控制方程关于卫星不确定参数呈线性化关系。最后,利用数值仿真模拟捕获过程系统运动状态,验证了上述鲁棒控制镇定运动的效果。     

绳系卫星在轨试验及地面物理仿真进展

通过系绳释放、运行和回收的在轨卫星称为绳系卫星. 绳系卫星功能独特, 在人工重力梯度、空间传送、电动力推进等方面应用广泛. 本文以绳系卫星为对象, 概述了全世界历年来绳系卫星的在轨飞行试验, 包括试验背景、目的、步骤以及结果等; 介绍了近年来绳系卫星的地面物理仿真实验技术, 分析了系统结构、仿真原理以及实验结果; 对未来我国空间绳系卫星技术的发展提出建议.     

D'alembert principle in the velocity space

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Nonlinear dynamics of flexible tethered satellite system subject to space environment

The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J ₂ perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multidegree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.     

Transport of phase space volume near isolated invariant sets

A measure preserving homeomorphismf determines a discrete dynamical system. Measurable sets in phase space are moved or transported byf. It is shown that the asymptotic rate of escape of phase space volume from neighborhoods which isolate the same invariant set is unique.     

Libration suppression of tethered space system with a moving climber in circular orbit

This paper studies the dynamics and libration suppression of a tethered system with a moving climber in circular orbits. The tethered system is modeled by a two-piece dumbbell model that consists of one main satellite, one climber and one end-body connected by two straight, massless and inextensible tethers. A new tension control strategy to suppress the libration of the tethered system due to the moving climber is proposed by reeling in-out tether at the end-body without thrust. The control strategy is implemented with the sliding mode control to suppress the libration angle of the climber to zero by the end of climber’s transfer phase. The numerical results show that the proposed control strategy is very effective in suppressing the libration of the climber in the three-body tethered system with tension control only. Furthermore, cases with limited tension control are examined. It reveals that a longer tether between the climber and the end-body is required to supplement the limited tension in suppressing the libration of the climber.     

Pendulum motions of extended lunar space elevator

In the usual everyday life, it is well known that the inverted pendulum is unstable and is ready to fall to “all four sides,” to the left and to the right, forward and backward. The theoretical studies and the lunar experience of moon robots and astronauts also confirms this property. The question arises: Is this property preserved if the pendulum is “very, very long”? It turns out that the answer is negative; namely, if the pendulum length significantly exceeds the Moon radius, then the radial equilibria at which the pendulum is located along the straight line connecting the Earth and Moon centers are Lyapunov stable and the pendulum does not fall in any direction at all. Moreover, if the pendulum goes beyond the collinear libration points, then it can be extended and manufactured from cables. This property was noted by F. A. Tsander and underlies the so-called lunar space elevator (e.g., see [1]). In the plane of the Earth and Moon orbits, there are some other equilibria which turn out to be unstable. The question is, Are there equilibria at which the pendulum is located outside the orbital plane? In this paper, we show that the answer is positive, but such equilibria are unstable in the secular sense. We also study necessary conditions for the stability of lunar pendulum oscillations in the plane of the lunar orbit. It was numerically discovered that stable and unstable equilibria alternate depending on the oscillation amplitude and the angular velocity of rotation. The study of the lunar elevator dynamics originates in [2]. The concept of lunar elevator was developed in detail in [3, 4]. Several classes of equilibria with the finiteness of the Moon size taken into account were studied in [5]. The possibility of location of an orbital station fixed to the Moon surface by a pair of tethers was investigated in [6]. The problem of orientation of the terminal station of the lunar space elevator was studied in [7]. The influence of the tether length variations on the motion of the lunar tether system was considered in [8]. The alternation of stable and unstable flat oscillations is well known in the problem of satellite oscillations in a circular orbit [9, 10].     

大型网架式可展开空间结构的非线性动力学与控制

我国航天工业迫切需要掌握可入轨后展开的大型网架式空间结构技术,以便研制口径十几米、乃至数十米的大型星载天线。该技术的主要科学基础是这类空间结构展开和服役过程的非线性动力学建模、分析和控制。本文综述了与上述科学基础相关的研究进展,提出应重点关注的三个科学问题：一是大型网架式空间结构展开过程的多柔体系统动力学,尤其是如何对微重力环境下索网的接触和缠绕、运动副内碰撞、结构展开与航天器本体间的耦合等导致的非线性动力学进行建模和分析;二是大型网架式空间结构展开锁定后服役的动力学分析,尤其是如何揭示结构柔性、众多运动副间隙、交变热载荷等因素引起的复杂非线性振动机理;三是大型网架式空间结构展开锁定后服役的动力学控制,尤其是如何在欠驱动、低能耗条件下对非线性振动和波动传播提出有效的控制方法。     

Conservation laws and symmetries of systems with unilateral constraints in phase space

By introducing the generalized quasi-symmetry of the infinitestinal transformation for transformation groupG _r , this paper studies the conservation laws and symmetries of dynamical systems with unilateral constraints in phase space. Noether's theorem and Noether's inverse theorem for mechanical systems with unilateral constraints in phase space are obtained and two kinds of equivalent forms of generalized Killing equations which are used to determine the generators of the infinitestinmal group transformation are given. The project sponsored by the National Natural Science Foundation and the Doctoral Programme Foundation of Institution of Higher Education of China.     

Numerical investigation of dynamical behavior of tethered rigid spheres in supersonic flow

The dynamical behavior of two tethered rigid spheres in a supersonic flow is numerically investigated. The tethered lengths and radius ratios of the two spheres are different. The two spheres, which are centroid axially aligned initially, are held stationary first, then released, and subsequently let fly freely in a supersonic flow. The mean qualities of the system and the qualities of the bigger sphere are considered and compared with the situations without the tether. In the separation process, six types of motion caused by the spheres, tether, and fluid interaction are found. The results show that the mean x-velocity of the system changes in a different manner for different radius ratios, and the x-velocity of the bigger sphere is uniformly reduced but through different mechanisms.     

Signal reconstruction by random sampling in chirp space

Reconstruction by irregular sampling and sampling at rates below the Nyquist rate are important issues for the experimental characterization of dynamical systems. For the space of functions that can be approximated by chirps, we prove a reconstruction theorem by random sampling at arbitrary rates.     

Stabilization of wave segments under a delayed feedback in the parameter space

Nonlinear Dynamics - We investigate the effects of delayed feedback on the stabilization of a propagating wave segment by introducing a dynamical subsystem in the parameter space. This method aims...     

Fundamental aspects of curvature indices for characterizing dynamical systems

It is important to characterize the properties of dynamical systems by a quantity that signifies their structural changes, in particular those associated with occurrence of chaos or other transitional behaviors. There are some well-known indices, such as Lyapunov exponent, fractal dimension, and Kolmogorov entropy, while in this article we use a new quantifier, named the curvature index, to study the dynamical systems. The curvature index (proposed by Chen and Chang in Chaos 22(2):371–383 2012) is defined as the limit of the average curvature of a trajectory during evolution for a dynamical system, which lumps all the bending effects of the trajectory to a number, and estimates its average size (such as an attractor) in virtue of an inscribed space ball. One may define N-1 curvature indices for an N-dimensional dynamical system. Once the system undergoes a structural change, there are corresponding changes in the first and/or higher curvatures. The study is aimed to examine fundamental aspects of the curvature indices with further applications to some outstanding examples of dynamical systems in the literature, in parallel to the analysis by the Lyapunov exponents.     

The state space reconstruction technology of different kinds of chaotic data obtained from dynamical system

Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail. The project supported by the National Natural Science Foundation of China (19672043)     

Advances in structural vibration control application of magneto-rheological visco-elastomer

Magneto-rheological visco-elastomer(MRVE)as a new smart material developed in recent years has several significant advantages over magneto-rheological liquid.The adjustability of structural dynamics to random environmental excitations is required in vibration control.MRVE can supply considerably adjustable damping and stiffness for structures,and the adjustment of dynamic properties is achieved only by applied magnetic fields with changeless structure design.Increasing researches on MRVE dynamic properties,modeling,and vibration control application are presented.Recent advances in MRVE dynamic properties and structural vibration control application including composite structural vibration mitigation under uniform magnetic fields,vibration response characteristics improvement through harmonic parameter distribution,and optimal bounded parametric control design based on the dynamical programming principle are reviewed.Relevant main methods and results introduced are beneficial to understanding and researches on MRVE application and development.