Displaced orbits generated by solar sails for the hyperbolic and degenerated cases

Displaced non-Keplerian orbits above planetary bodies can be achieved by orientating the solar sail normal to the sun line. The dynamical systems techniques are employed to analyze the nonlinear dynamics of a displaced orbit and different topologies of equilibria are yielded from the basic configurations of Hill’s region, which have a saddlenode bifurcation point at the degenerated case. The solar sail near hyperbolic or degenerated equilibrium is quite unstable. Therefore, a controller preserving Hamiltonian structure is presented to stabilize the solar sail near hyperbolic or degenerated equilibrium, and to generate the stable Lissajous orbits that stay stable inside the stabilizing region of the controller. The main contribution of this paper is that the controller preserving Hamiltonian structure not only changes the instability of the equilibrium, but also makes the modified elliptic equilibrium become unique for the controlled system. The allocation law of the controller on the sail’s attitude and lightness number is obtained, which verifies that the controller is realizable.     

Trajectory optimization and applications using high performance solar sails

The high performance solar sail can enable fast missions to the outer solar system and produce exotic non-Keplerian orbits. As there is no fuel consumption, mission trajectories for solar sail spacecraft are typically optimized with respect to flight time. Several investigations focused on interstellar probe missions have been made, including optimal methods and new objective functions. Two modes of interstellar mission trajectories, namely “direct flyby” and “angular momentum reversal trajectory”, are compared and discussed. As a foundation, a 3D non-dimensional dynamic model for an ideal plane solar sail is introduced as well as an optimal control framework. A newly found periodic double angular momentum reversal trajectory is presented, and some properties and potential applications of this kind of inverse orbits are illustrated. The method how to achieve the minimum periodic inverse orbit is also briefly elucidated.     

燃料大幅晃动等几何分析仿真及航天器耦合动力学研究

现代航天器肩负许多周期长且复杂的航天任务,通常需要携带大量的液体燃料.贮箱中液体燃料大幅晃动会严重影响航天器的姿态稳定性和控制精度,是现代航天器耦合动力学建模和精确控制研究的重要问题.本文提出了一种新的液体大幅晃动数值仿真方法,采用等几何分析方法对贮箱内气体和液体整体进行建模和空间离散,采用压力修正的分步法对控制方程进行时间离散,结合水平集方法划分气体和液体区域并且实时追踪液体晃动自由面.提出了一种质量修正方法以消除水平集函数演化产生的液体质量误差.基于燃料大幅晃动等几何分析仿真方法,对携带太阳能帆板的充液航天器进行动力学建模和耦合运动数值仿真.对于太阳能帆板的振动问题则采用Kirchhoff-Love板理论建模和模态分析法数值求解.通过将数值仿真结果与解析解对比,证明了本文给出方法的正确性.本文还对燃料大幅晃动下的航天器刚-液-柔耦合运动进行了数值仿真,发现液体晃动对航天器的姿态变化和结构振动的幅值和频率具有不可忽视的影响.     

Analytical method for the attitude stability of partially liquid filled spacecraft with flexible appendage

In this paper, the attitude stability of liquid-filled spacecraft with flexible appendage is investigated. The motion of liquid sloshing is modeled as the spherical pen-dulum, and the flexible appendage is approached by a linear shearing beam. Nonlinear dynamic equations of the coupled system are derived from the Hamiltonian. The stability of the coupled system was analyzed by using the energy-Casimir method, and the nonlinear stability theorem of the coupled spacecraft system was also obtained. Through numerical computation, the correctness of the proposed theorem is verified and the boundary curves of the stable region are presented. The increase of the angular velocity and flexible attachment length will weaken the attitude stability, and the change of the filled ratio of liquid fuel tank has a different influence on the stability of the coupled spacecraft, depend-ing on the different conditions. The attitude stability analysis of the coupled spacecraft system in this context is useful for selecting appropriate parameters in the complex spacecraft design.     

两尺度Duffing系统的动力吸振器减振研究

两尺度耦合的Duffing系统存在复杂振动, 此类振动具有振幅大、频率高的特点, 对系统的危害不容忽视. 研究了线性动力吸振器对低频参数激励下Duffing系统的振动控制问题, 通过对比耦合动力吸振器前后系统的时间历程图、相图, 发现加入动力吸振器后系统会由单一振动模式转变为混合振动模式(簇发振动), 振动幅值明显减小, 尤其对高频振动部分抑制明显. 利用快慢分析法, 当参数激励为慢变过程时得到相应的自治系统, 并发现自治系统稳定性与分岔行为对非自治系统振动响应具有明显调节作用. 研究结果表明, 虽然耦合动力吸振器前后自治系统均发生叉形分岔, 但是加入吸振器后自治系统稳定性发生变化, 稳定中心变为渐进稳定的焦点, 稳定平衡线对非自治系统轨线的吸引力增强, 使得响应振动幅值减小; 另外轨线在不同吸引子之间的跳跃次数减少, 也是导致响应振动幅值减小的另一个原因. 通过对参数激励的相关参数减振效果分析, 发现加入的动力吸振器在较大的振动幅值和频率范围内都能起到抑制系统振动的作用. 为两尺度系统耦合线性动力吸振器减振研究提供了理论依据.      

非自旋航天器混沌姿态运动及其参数开闭环控制

研究万有引力场中受大气阻力且存在结构内阻尼的非自旋航天器在椭圆轨道上平面天平动的混沌及其参数开闭环控制问题．在建立数学模型的基础上确定出现混沌的必要条件并数值验证混沌的存在性，提出非线性振动系统混沌运动的参数开闭环控制并应用于控制航天器的混沌姿态运动．     

Formation around planetary displaced orbit

The paper investigates the relative motion around the planetary displaced orbit. Several kinds of displaced orbits for geocentric and martian cases were discussed. First, the relative motion was linearized around the displaced orbits. Then, two semi-natural control laws were investigated for each kind of orbit and the stable regions were obtained for each case. One of the two control laws is the passive control law that is very attractive for engineering practice. However, the two control laws are not very suitable for the Martian mission. Another special semi-natural control law is designed based on the requirement of the Martian mission. The results show that large stable regions exist for the control law.     

Motion of the moonlet in the binary system 243 Ida

The motion of the moonlet Dactyl in the binary system 243 Ida is investigated in this paper. First, periodic orbits in the vicinity of the primary are calculated, including the orbits around the equilibrium points and large-scale orbits. The Floquet multipliers' topological cases of periodic orbits are calculated to study the orbits' stabilities. During the continuation of the retrograde near-circular orbits near the equatorial plane, two period-doubling bifurcations and one Neimark–Sacker bifurcation occur one by one, leading to two stable regions and two unstable regions. Bifurcations occur at the boundaries of these regions. Periodic orbits in the stable regions are all stable, but in the unstable regions are all unstable. Moreover, many quasi-periodic orbits exist near the equatorial plane. Long-term integration indicates that a particle in a quasi-periodic orbit runs in a space like a tire. Quasi-periodic orbits in different regions have different styles of motion indicated by the Poincare sections. There is the possibility that moonlet Dactyl is in a quasi-periodic orbit near the stable region I, which is enlightening for the stability of the binary system.     

Stability and control of tethered satellite with chemical propulsion in orbital plane

The tethered satellite with chemical propulsion has broad application prospects in the disposal of abandoned satellites, the orbital rescue of spacecrafts, and the transportation of space supplies, which is completely different from the traditional applications of tethered satellites. Therefore, new research on its dynamics, stability, and control becomes useful and interesting. In this article, based on a dumbbell model of tethered satellite, the dynamics equations of tethered system in orbital maneuvering are established. Furthermore, according to the definitions of transversal and radial propulsive coefficients, analytical solutions of the equilibrium position for librational angle are derived during maneuvering in orbital plane; meanwhile, the effects of propulsive coefficients on librational stability are analyzed, which provides a basis for a selection of expected attitude trajectory. Then, a method of hierarchical sliding-mode tension control is presented to track the expected in-plane angle. This method can address the underactuated problem of tethered systems without either complex coordinate transformation for the system state model or constraint equation restrictions. During orbital flight, in-plane and out-of-plane angles are decoupled, so the tether tension control cannot be conducted to inhibit the out-of-plane angle. To solve this problem, the binormal component of thrust acceleration normal to the orbital plane is adopted as a control variable, and a feedback linearization-based thrust controller is designed to damp out the out-of-plane angle. Afterwards, orbital transfer cases between two circular orbits are studied to demonstrate the effectiveness of the tethered satellite with chemical propulsion. Numerical simulation results indicate that the stability of librational angles has a close relation to propulsive coefficients, and distributions of stable centers and unstable saddle points are totally different on both sides of bifurcation point. In addition, tracking control requirements for tethered satellite are guaranteed by designed controllers, which ensure flight safety in orbital maneuvering.     

太阳帆日心悬浮轨道附近的相对运动

研究悬浮轨道附近的编队飞行问题,推导了悬浮轨道附近的相 对运动方程. 由于编队太阳帆之间的距离与帆到太阳的距离的比值为小量,将相对运动方程 在悬浮轨道附近线性化,得到了线性化方程. 基于该线性化方程,考虑了悬浮轨道附近的几 种编队控制方法,只需通过调节太阳帆的姿态来进行简单的控制. 其中包括一种被动编队控 制策略,该控制策略具有实现简单、稳定区域大的特点,具有很好的工程应用前景. 最后基 于非线性方程对每种编队策略进行了数值仿真验证,数值结果表明该控制方法能实现编 队.     

航天器太阳帆板振动抑制的输入整形方法研究

利用输入整形与PD(比例微分)控制相结合的主动振动控制策略,在保证航天器完成三轴姿态机动的同时抑制太阳帆板的振动。首先,基于角动量定律和拉格朗日法建立了带挠性太阳帆板航天器的动力学模型。然后,在动力学模型的基础上,采用PD控制作为航天器三轴姿态机动的控制策略,利用挠性太阳帆板各阶模态的固有频率和阻尼比得到系统的输入整形器,对原始姿态机动的脉冲进行输入整形前馈控制,以抑制太阳帆板各阶模态的振动。仿真结果表明:两种输入整形方法均能抑制太阳帆板的振动,ZV(零残余振动)输入整形器简单且脉冲数量少,输入时间较短,但对于参数摄动以及输入的微小误差比较敏感,抑制振动的效果难以满足零残余振动的标准;ZVD(微分零残余振动)输入整形器脉冲数量较多,具有一定量的延时,但更为高效,鲁棒性强,能够极大地抑制挠性太阳帆板的残余振动,缩短航天器的机动稳定时间,且整个机动过程更加平稳。     

Nonlinear dynamics of a satellite with deployable solar panel arrays

The multibody dynamics of a satellite in circular orbit, modeled as a central body with two hinge-connected deployable solar panel arrays, is investigated. Typically, the solar panel arrays are deployed in orbit using preloaded torsional springs at the hinges in a near symmetrical accordion manner, to minimize the shock loads at the hinges. There are five degrees of freedom of the interconnected rigid bodies, composed of coupled attitude motions (pitch, yaw and roll) of the central body plus relative rotations of the solar panel arrays. The dynamical equations of motion of the satellite system are derived using Kane's equations. These are then used to investigate the dynamic behavior of the system during solar panel deployment via the 7-8th-order Runge-Kutta integration algorithms and results are compared with approximate analytical solutions. Chaotic attitude motions of the completely deployed satellite in circular orbit under the influence of the gravity-gradient torques are subsequently investigated analytically using Melnikov's method and confirmed via numerical integration. The Hamiltonian equations in terms of Deprit's variables are used to facilitate the analysis.     

Attitude tracking control of flexible spacecraft with large amplitude slosh

This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli–Euler beam, and the assumed modal method is employed.A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics,liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking.     

THE EVOLUTION CHARACTERIZATION OF LIBRATIN POINT ORBITS AND APPLICATION RESEARCH

三体问题中, 轨道的受力和运动规律非常复杂. 对于特定的任务, 如何选择轨道的初始解是一大难题.针对平面三体问题, 利 用近拱点庞加莱映射, 对平动点顺行轨道和逆行轨道的长期和短期演化性质进行分析.根据轨道的初始状态将其分为逃逸轨道和捕获轨道.对于逃逸轨道, 给出了同宿轨道和异宿轨道的设计方法, 并利用两级微分修正法消除了拼接点处的位置不连续问题.对于捕获轨道, 得到了几类典型的周期和准周期轨道.对逆行轨道的演化性质进行分析时发现, 逆行轨道通常为准周期轨道, 比顺行轨道更加稳定.利用近拱点庞加莱映射可以快速确定不同类型轨道对应的初始状态, 为特定任务需求下的轨道设计提供了一种快速而有效的选择方案.     

条带式太阳帆的结构动力学分析

依靠光压推进,太阳帆被认为是最可行的星际探测航天器,太阳帆结构总体方案主要有两类:桅杆式和旋转式,其中,帆膜被分割成窄条的条带式太阳帆在桅杆式太阳帆中具有较为理想的结构效率,如何准确计算条带式太阳帆的结构动力学特性值得研究.本文对条带式太阳帆结构的振动特性和结构稳定性进行研究,将太阳帆看作是由若干个桅杆-膜带组件依次连接而成的整体结构,桅杆-膜带组件由4根桅杆段和4条薄膜条带组成,分段轴压作用下的桅杆与薄膜条带耦合振动.考虑帆面薄膜条带与支撑桅杆之间的耦合振动,采用分布传递函数法建立了的条带式太阳帆的结构动力学模型,推导了条带式太阳帆结构自由振动和失稳载荷的求解方法.研究表明:条带式太阳帆构型有利于提高太阳帆结构的整体刚度和结构稳定性,随着帆面薄膜条带数目的增加,太阳帆结构的振动频率和失稳载荷增大;随着帆面薄膜预应力的增大,太阳帆结构振动的基频减小,稳定性变差;随着支撑桅杆刚度的提高,太阳帆结构整体的振动频率和失稳载荷增大.本文建立的解析求解方法具有求解效率快和精度高的特点,为条带式太阳帆的结构设计和姿态控制提供了有力的分析工具.      

MODEL OF CENTRIFUGAL EFFECT AND ATTITUDE MANEUVER STABILITY OF A COUPLED RIGID-FLEXIBLE SYSTEM

IntroductionThedynamicandcontrolofcoupledrigid_flexiblesystemisaleading_edgeresearchsubjectthathasdrawnextensiveattentionfromtheacademiccommunityintheworld[1].TheresearchconductedbyKaneetal.in 1 987[2 ]suggestedthat,thetraditionalmodelapplyingstructuraldynamicsassumptionaboutelasticdeformationindiscriminately[3,4 ],ineffect,hasneglectedtheso_called“dynamicstiffening”effectresultedfromcoupledrigid_flexiblesystem .Therefore ,itisofparticularimportancetoresearchtheactionofcoupledrigid_flexibles…     

Forced resonance orbit analysis of binary asteroid system with consideration of solar radiation pressure

The solar radiation pressure is one of the major perturbations to orbits in the study of binary asteroid system, since asteroids have relatively weak gravity fields. In this paper, based on the idea of treating the solar radiation pressure as periodic external excitation, one novel family of orbits due to primary resonance and another novel family of orbits due to both primary resonance and internal resonance have been found by the classical perturbation method. The two types of steady-state orbits due to external resonance with different area-to-mass ratios have been determined and discussed by the frequency–response equations analytically. Four binary asteroid systems, 283 Emma-S/2003 (283) 1, 22 Kalliope-Linus, 2006 Polonskaya-S/2005 (2006) 1 and 4029 Bridges have been taken as examples to show the validity of the proposed mechanism in the explanation of orbits formation due to resonance. The multiple shooting method is applied to obtain the resonance orbits after numerical iterations.

     

The dynamics of coupled planar rigid bodies. II. Bifurcations,periodic solutions,and chaos

We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.     

Influence of flexible solar arrays on vibration isolation platform of control moment gyroscopes

A high-performance vibration isolation platform (VIP) has been developed for a cluster of control moment gyroscopes (CMGs). CMGs have long been used for satellite attitude control. In this paper, the influence of flexible solar arrays on a passive multi-strut VIP of CMGs for a satellite is analyzed. The reasonable parameters design of flexible solar arrays is discussed. Firstly, the dynamic model of the integrated satellite with flexible solar arrays, the VIP and CMGs is conducted by Newton-Euler method. Then based on reasonable assumptions, the transmissibility matrix of the VIP is derived. Secondly, the influences of the flexible solar arrays on both the performance of the VIP and the stability of closed-loop control systems are analyzed in detail. The parameter design limitation of these solar arrays is discussed. At last, by selecting reasonable parameters for both the VIP and flexible solar arrays, the attitude stabilization performance with vibration isolation system is predicted via simulation.     

双小行星探测轨道动力学研究进展

双小行星系统由在万有引力作用下彼此环绕的两颗小行星组成, 对研究太阳系起源、行星系统演化和行星防御都具有重要的价值, 近年来成为行星科学和航天动力学研究的热门对象, 对双小行星系统的原位探测也即将迎来热潮. 双小行星系统的独特构型和附近的复杂动力学环境为探测器轨道动力学和任务设计带来了全新的挑战, 为应对这些挑战所进行的研究也推动了轨道动力学基础理论的发展. 本文对双小行星探测轨道动力学的研究进展进行综述, 首先介绍了双小行星研究和探测的背景及意义, 简要阐述了双小行星系统形成理论及其附近轨道动力学的研究概况. 其次, 介绍了双小行星系统不规则引力场和相互引力势的建模方法, 进而展示了双星的姿态轨道耦合动力学, 即完全二体问题, 包括双星相对运动的平衡构型和稳定性. 接着, 介绍了描述双星附近探测器轨道运动的限制性完全三体问题的动力学模型, 以及该模型下的平动点、平动点周期轨道、大范围周期轨道、转移轨道和轨道维持等方面的研究进展. 第四部分综述了环绕双小行星系统单颗星的受摄二体问题, 以轨道摄动理论和行星系统中受摄二体问题的研究现状为背景, 介绍了环绕双小行星系统主星的半解析轨道动力学建模与轨道稳定性分析. 之后, 介绍了目前面向探测任务需求和考虑实际约束的轨道动力学研究和轨道设计. 最后, 基于目前研究进展, 分析了面临的若干问题, 对未来双小行星探测轨道动力学及相关技术的发展进行了讨论和展望.