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.     

COLLINEAR LIBRATION POINTS WITH CONTINUOUS LOW THRUST

研究了圆型限制性三体问题的平动点在连续小推力作用下的具体位置和动力学特征的变化. 研究表明,随着小推力方向在空间中的变化,平动点的具体位置也会发生相应的变化,文章详细阐述了这些变化的特征.针对航天任务中应用较多的共线平动点L1和L2,研究了其附近运动的稳定性状态,给出了线性条件稳定解,并在此基础上,构造了条件稳定解的高阶形式,将其结果与数值积分轨道进行了比对,两者符合得很好. 最后,进一步研究了共线平动点附近周期轨道族的演化状态,由于连续小推力引入的非对称性,周期轨道族会发生分岔现象.     

Multi-modes control method for spacecraft formation establishment and reconfiguration near the libration points

This paper studies Multi-modes control method for libration points formation establishment and reconfiguration. Firstly, relations between optimal impulse control and Floquet modes are investigated. Method of generating modes is proposed. Characteristics of the mode coefficients stimulated at different time are also given. Studies show that coefficients of controlled modes can be classified into four types, and formation establishment and reconfiguration can be achieved by multi-impulse control with the presented method of generating modes. Then, since libration points formation is generally unstable, mutli-modes keeping control method which can stabilize five Floquet modes simultaneously is proposed. Finally, simulation on formation establishment and reconfiguration are carried out by using method of generating modes and mutli-modes keeping control method. Results show that the proposed control method is effective and practical.     

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.     

Impact of the interplanetary magnetic field on thewave flow pattern in the neighborhood of the Earth’s bow shock under sharp variations in the solar wind dynamic pressure

The impact of the interplanetary magnetic field on transformation and disintegration of the Earth’s bow shock into a system of magnetohydrodynamic (MHD) shock waves, rotational discontinuities and rarefaction waves under the action of abrupt variations in the solar wind dynamic pressure is simulated in the three-dimensional non-plane-polarized formulation within the framework of the ideal magnetohydrodynamic model using the solution of the MHD Riemann problem of breakdown of an arbitrary discontinuity. This discontinuity arises when a contact discontinuity, on which the solar wind density increases or decreases suddenly and which travels together with the solar wind, impinges on the Earth’s bow shock and propagates along its surface. The interaction pattern is constructed in the quasisteady- state formulation as a mosaic of exact solutions obtained on computer using an original MHD Riemann solver. The wave flow patterns are found for all elements of the surface of the bow shock as functions of their latitude and longitude for various jumps in the density on the contact discontinuity and characteristics parameters of the solar wind and interplanetary magnetic field at the Earth’s orbit. It is found that when the solar wind dynamic pressure increases, a fast MHD shock wave, that first penetrates into the magnetosheath, is always formed. When the solar wind dynamic pressure decreases, the influence of the interplanetary magnetic field can lead to the development of the leading fast MHD shock wave in certain zones on the surface of the Earth’s bow shock. The solution obtained can be used to interpret measurements on spacecraft in the solar wind at the libration point and in the neighborhood of the Earth’s magnetosphere.     

Time-optimal rendezvous transfer trajectory for restricted cone-angle range solar sails

The advantage of solar sails in deep space exploration is that no fuel consumption is required. The heliocentric distance is one factor influencing the solar radiation pressure force exerted on solar sails. In addition, the solar radiation pressure force is also related to the solar sail orientation with respect to the sunlight direction. For an ideal flat solar sail, the cone angle between the sail normal and the sunlight direction determines the magnitude and direction of solar radiation pressure force. In general, the cone angle can change from 0° to 90°. However, in practical applications, a large cone angle may reduce the efficiency of solar radiation pressure force and there is a strict requirement on the attitude control. Usually, the cone angle range is restricted less more than an acute angle （for example, not more than 40°） in engineering practice. In this paper, the time-optimal transfer trajectory is designed over a restricted range of the cone angle, and an indirect method is used to solve the two point boundary value problem associated to the optimal control problem. Relevant numerical examples are provided to compare with the case of an unrestricted case, and the effects of different maximum restricted cone angles are discussed. The results indicate that （1） for the condition of a restricted cone-angle range the transfer time is longer than that for the unrestricted case and （2） the optimal transfer time increases as the maximum restricted cone angle decreases.     

日地系统L_2点Halo轨道绳系卫星编队动力学

研究平动点附近周期轨道上旋转多体绳系卫星编队系统的非线性耦合动力学问题。编队系统为各卫星质量接近的轮辐状结构,位于日地系统第二平动点附近,整个系统的旋转保持系绳处于张紧状态,建立Hill限制性三体问题的绳系编队系统动力学模型。针对处于留位阶段的典型对称三星编队,在位于较大Halo轨道上无控制力作用的情况下,进行母卫星轨道运动与系绳摆动耦合运动的动力学模拟,分析轨道方向、卫星质量比、系绳长度以及初始旋转速度对编队系统整体稳定性的影响。     

一种形成尾翼型聚能侵彻体新方法的实验研究

尾翼可以提高聚能侵彻体的飞行稳定性,如何形成有一定规律性的尾翼在聚能侵彻体的研究中具有重要意义。在药型罩上粘附隔板,利用隔板改变爆轰波波阵面的结构形状,使药型罩上的爆轰压力发生规律变化,从而发生规律性的变形,最终形成带有尾翼的聚能侵彻体,这是一种新的形成尾翼的方法。从药型罩微元压垮速度变化和药型罩表面爆轰压力变化的角度出发,对新方法形成尾翼的机理进行了初步探讨。通过合理设计隔板的几何尺寸对该方法形成尾翼型聚能侵彻体进行试验,试验回收到了带有尾翼的聚能侵彻体,说明新方法形成尾翼具有一定的可行性。     

基于多项式约束的三角平动点平面周期轨道设计方法1）

平动点是圆型限制性三体问题中的五个平衡解.其中,三角平动点在平面问题中具有“中心×中心”的动力学特性,其附近存在着大量的周期轨道,研究这些周期轨道的构建方法在深空探测中具有理论及工程意义.本文从振动角度分析周期轨道,通过多项式展开法构建出主坐标下周期轨道两个运动方向之间的渐近关系.从新的角度分析了系统的动力学特性和平面周期运动两个方向内在关联以及物理规律.这种多项式形式的关系式,可以作为约束条件用于数值微分修正算法中,通过迭代的方式寻找周期轨道.数值仿真算例验证了方法的正确性及精确性.文章从振动的角度对周期轨道进行分析,改进了微分修正算法.提出的方法可以被拓展至圆型/椭圆型限制性三体问题的三维周期轨道构建中.     

最优轨迹规划方法及其平动点航天器编队均衡耗能重构应用

由于均衡耗能航天器编队能够提高整体航天器编队服役时间,针对平动点航天器编队重构的均衡耗能最优轨迹规划问题,提出一种以状态、协态和控制三类变量插值为核心的求解非线性最优控制问题的新方法。基于连续时间表达的非线性最优控制问题通过变分原理转化为非线性方程组的求解,并进一步推导非线性方程组显示格式的Jacobi矩阵提高非线性方程组的计算效率。本文方法既满足最优控制理论的一阶必要条件又具有较大的收敛域;同时,不需要对协态初值准确猜测,避免了大规模非线性规划问题的求解。通过对中心航天器位置固定和无中心航天器两种情况的数值模拟,结果表明,本文方法对航天器编队重构轨迹规划问题能够达到均衡耗能的目标,具有一定的应用价值。     

Optimal nonlinear feedback control of spacecraft rendezvous with finite low thrust between libration orbits

This paper presents the nonlinear closed-loop feedback control strategy for the spacecraft rendezvous problem with finite low thrust between libration orbits in the Sun–Earth system. The model of spacecraft rendezvous takes the perturbations in initial states, the actuator saturation limits, the measurement errors, and the external disturbance forces into consideration from an engineering point of view. The proposed nonlinear closed-loop feedback control strategy is not analytically explicit; rather, it is implemented by a rapid re-computation of the open-loop optimal control at each update instant. To guarantee the computational efficiency, a novel numerical algorithm for solving the open-loop optimal control is given. With the aid of the quasilinearization method, the open-loop optimal control problem is replaced successfully by a series of sparse symmetrical linear equations coupled with linear complementary problem, and the computational efficiency can be significantly increased. The numerical simulations of spacecraft rendezvous problems in the paper well demonstrate the robustness, high precision, and dominant real-time merits of the proposed closed-loop feedback control strategy.     

Passive morphing of flying wing aircraft: Z-shaped configuration

High Altitude, Long Endurance (HALE) aircraft can achieve sustained, uninterrupted flight time if they use solar power. Wing morphing of solar powered HALE aircraft can significantly increase solar energy absorbency. An example of the kind of morphing considered in this paper requires the wings to fold so as to orient a solar panel to be hit more directly by the sun's rays at specific times of the day. An example of the kind of morphing considered in this paper requires the wings to fold so as to orient a solar panel that increases the absorption of solar energy by decreasing the angle of incidence of the solar radiation at specific times of the day. In this paper solar powered HALE flying wing aircraft are modeled with three beams with lockable hinge connections. Such aircraft are shown to be capable of morphing passively, following the sun by means of aerodynamic forces and engine thrusts. The analysis underlying NATASHA (Nonlinear Aeroelastic Trim And Stability of HALE Aircraft), a computer program that is based on geometrically exact, fully intrinsic beam equations and a finite-state induced flow model, was extended to include the ability to simulate morphing of the aircraft into a “Z” configuration. Because of the “long endurance” feature of HALE aircraft, such morphing needs to be done without relying on actuators and at as near zero energy cost as possible. The emphasis of this study is to substantially demonstrate the processes required to passively morph a flying wing into a Z-shaped configuration and back again.     

Periodic motion around libration points in the Elliptic Restricted Three-Body Problem

Periodicity of motion around the collinear libration point associated with the Elliptic Restricted Three-Body Problem is studied. A survey of periodic solutions in the Circular Restricted Three-Body Problem is presented considering both Sun–Earth and Earth–Moon systems. Halo, Lyapunov and Vertical families around L1, L2 and L3 points are investigated, and their orbital period ranges through the entire family are reported. Resonant motions within the orbit families in the circular problem are identified and selected as suitable initial guess to find periodic orbits in the elliptic problem, which are targeted using a differential correction algorithm. Periodic solutions found are cataloged depending on the number of revolutions around libration points. Geometry, dynamical behavior and stability properties of single-revolution orbits are shown, as well as double-, triple- and quadruple-revolution solutions.     

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.

     

A new control law based on characteristic exponent assignment for libration point orbit maintenance

A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.     

Spacecraft motion around artificial equilibrium points

The main goal of this paper is to describe the motion of a spacecraft around an artificial equilibrium point in the circular restricted three-body problem. The spacecraft is under the gravitational influence of the Sun and the Earth, as primary and secondary bodies, subjected to the force due to the solar radiation pressure and some extra perturbations. Analytical solutions for the equations of motion of the spacecraft are found using several methods and for different extra perturbations. These solutions are strictly valid at the artificial equilibrium point, but they are used as approximations to describe the motion around this artificial equilibrium point. As an application of the method, the perturbation due to the gravitational influence of Jupiter and Venus is added to a spacecraft located at a chosen artificial equilibrium point, near the \(L_3\) Lagrangian point of the Sun–Earth system. The system is propagated starting from this point using analytical and numerical solutions. Comparisons between analytical–analytical and analytical–numerical solutions for several kinds of perturbations are made to guide the choice of the best analytical solution, with the best accuracy.     

Numerical heat transfer in a cavity with a solar control coating deposited to a vertical semitransparent wall

A transient two‐dimensional computational model of combined natural convection, conduction, and radiation in a cavity with an aspect ratio of one, containing air as a laminar and non‐participating fluid, is presented. The cavity has two opaque adiabatic horizontal walls, one opaque isothermal vertical wall, and an opposite semitransparent wall, which consists of a 6‐mm glass sheet with a solar control coating of SnS–Cu_xS facing the cavity. The semitransparent wall also exchanges heat by convection and radiation from its external surface to the surroundings and allows solar radiation pass through into the interior of the cavity. The momentum and energy equations in the transient state were solved by finite differences using the alternating direction implicit (ADI) technique. The transient conduction equation and the radiative energy flux boundary conditions are coupled to these equations. The results in this paper are limited to the following conditions: 10⁴≤Gr≤10⁶, an isothermal vertical cold wall of 21°C, outside air temperatures in the range 30°C≤T₀≤40°C and incident solar radiation of AM2 (750 W m⁻²) normal to the semitransparent wall. The model allows calculation of the redistribution of the absorbed component of solar radiation to the inside and outside of the cavity. The influences of the time step and mesh size were considered. Using arguments of energy balance in the cavity, it was found that the percentage difference was less than 4 per cent, showing a possible total numerical error less than this number. For Gr=10⁶ a wave appeared in the upper side of the cavity, suggesting the influence of the boundary walls over the air flow inside the cavity. A Nusselt number correlation as a function of the Rayleigh number is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Thrust generation and wake structure of wiggling hydrofoil

Marine animals and micro-machines often use wiggling motion to generate thrust. The wiggling motion can be modeled by a progressive wave where its wavelength describes the flexibility of wiggling animals. In the present study, an immersed boundary method is used to simulate the flows around the wiggling hydrofoil NACA 65-010 at low Reynolds numbers. One can find from the numerical simulations that the thrust generation is largely determined by the wavelength. The thrust coefficients decrease with the increasing wavelength while the propulsive efficiency reaches a maximum at a certain wavelength due to the viscous effects. The thrust generation is associated with two different flow patterns in the wake： the well-known reversed Karman vortex streets and the vortex dipoles. Both are jet-type flows where the thrust coefficients associated with the reversed Karman vortex streets are larger than the ones associated with the vortex diploes.     

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.      

Contouring spike nozzles and determining the optimal direction of their primary flows

Problems related with the optimal contouring of two-dimensional and axisymmetric spike nozzles providing maximum thrust for given dimensions and external pressure are studied. The nozzles under consideration are self-adjustable which is ensured by the non-zero inclination of their primary supersonic flow to the plane (axis) of symmetry. Along with the optimal contouring of the spike, the optimal orientation of the “primary” nozzle producing the primary flow is obtained. In the exact formulation, its optimal inclination is determined by an exhaustive search for the configurations providing maximum thrust for a given spike length and various fixed inclinations of the primary nozzle. The spike and primary nozzle contours of these configurations are generally joined through a bend with the formation of an expansion fan in the flow around the bend. The efficiency of a simpler approximate method for contouring the spike and determining a near-optimal inclination of the primary nozzle is demonstrated. The method is based on passage to a modified formulation of the problem differing from the original one in that it is only the part of the spike extending beyond the primary nozzle edge that is preassigned rather than its entire length. In the modified formulation, there is no a bend in the flow around which an expansion fan could be formed, while the inclination of the primary nozzle is determined in the process of designing the unique optimal configuration.