Closed form perturbation solution of a fast rotating triaxial satellite under gravity-gradient torque

The attitude dynamics of a fast rotating triaxial satellite under gravity-gradient is revisited. The essentially unique reduction of the Euler-Poinsot Hamiltonian, which can be performed in different sets of variables, provides a suitable set of canonical variables that expedites the perturbation approach. Two canonical transformations reduce the perturbed problem to its secular terms. The secular Hamiltonian and the transformation equations of the averaging are computed in closed form of the triaxiality coefficient, thus being valid for any triaxial body. The solution depends on Jacobi elliptic functions and integrals, and applies to non-resonant rotations under the assumption that the rotation rate is much higher than the orbital or precessional motion.     

带多充液圆柱贮箱航天器刚-液耦合动力学研究

文中以在低重环境下带多充液圆柱贮箱刚性航天器中刚-液耦合方程的建立和求解为主要研究目的。推导航天器中充液圆柱贮箱内任意点的牵连运动方程,根据壁面边界条件给出了贮箱内液体牵连晃动势的表达式;利用第二类边界条件下的傅立叶-贝塞尔级数展开法对低重力环境下的弯曲自由液面处的复杂动力学边界条件进行处理,建立以液体相对晃动势的模态坐标和晃动波高的模态坐标为状态向量的液体耦合晃动力学方程,通过积分分别得到了耦合晃动力和耦合晃动力矩的解析式;运用准坐标系下的拉格朗日方程建立以航天器主刚体姿态坐标和轨道坐标为状态向量的刚体耦合运动动力学方程,进一步联立上述耦合方程得到航天器整体系统的刚-液耦合动力学状态方程;最后,编制出适用于带多充液圆柱贮箱航天器内刚-液耦合动力学计算的模块化计算程序,通过计算实例验证所编程序的准确性的同时,研究了携带多充液箱航天器系统贮箱布局、外激励方式对航天器刚-液耦合系统动力学特性的影响。     

Luni-solar perturbations in the extended phase space representation of the Vinti problem

Perturbation theory is applied to the Vinti problem—motion about an oblate spheroid—to include the gravitational effects of the sun and moon. The problem is formulated using the extended phase space method which introduces a new independent variable similar to the true anomaly. The disturbing Hamiltonian H₁ for third bodies is of order J₂² (second order) and the final goal is a theory including second order short and long period terms and third order secular terms. The current paper however carries the development only to the second order in the secular terms and the first order in the periodic terms. Problems of including the higher orders are discussed. Therefore, in the development of H₁ all terms of order 10^?9 or larger are retained. The lunar emphemeris retains terms to e′² in the lunar eccentricity. The perturbation analysis is carried out by means of Lie series and is developed through the first order only which is consistent with the final accuracy desired. The generating function W₁ is obtained and separated into the long period, short period and secular terms. From W₁ the coordinates are defined from the Lie series by means of a transformation equation. These coordinates are non-singular for small eccentricity and inclination. Because of the complexity of the equations all algebraic computations were accomplished by means of a computerized Poisson series manipulator developed at the Naval Research Laboratory.     

轨道机动的时间-能量综合最优控制

围绕航天器快速精确轨道机动问题,探讨在持续小推力作用下,航天器轨道机动中时 间和能量综合最优控制的技术和方法。基于Pontryagin最小(大)值原理,针对目标轨道为平 面和空间椭圆的情况,推导了时间-能量综合最优控制的Hamilton正则方程组、终端条件 、横截条件和最优控制的表达式,应用数值方法求解正则微分方程组的两点边值问题,得到 了最优控制的数值解,包括最小时间、最小能量、最优轨道、最优控制时变曲线和最优反馈 控制曲线等,实现轨道机动最优控制的精确数值模拟。从数值结果的对比分析中得出了一些 有意义的结论,可供工程实际参考。
     

一种新的共线平动点拟周期轨道稳定保持策略

限制性三体问题下共线平动点附近的拟周期轨道在深空探测中具有重要的实际应用价值,得到了各航天大国的广泛重视。通过将动力学中心流形结构引入轨道控制方法的设计之中,得到了基于投影到中心流形的共线平动点拟周期轨道稳定保持策略。首先推导了会合坐标到中心流形坐标的正则变换方法,在此基础上设法通过引入轨道机动,将偏差状态点投影到中心流形上,从而达到消除不稳定分量的目的。该方法充分整合了平动点的动力学特性,并且也适用于周期轨道的稳定保持。通过对Lissajous轨道和晕轨道的数值仿真表明,该方法较以往方法具有更强的稳定性,能在显著降低轨控燃料消耗的基础上达到较好的稳定保持效果。     

Formation design in elliptical orbit using relative orbit elements

A new set of relative orbit elements is strictly defined through spherical geometry. The exact transformation equations between the new relative orbit elements and classical-orbital elements are derived. A new relative motion model with no singularity problem is derived based on the relative orbit elements, which are suitable for both elliptical and circular reference orbits. The in-plane and out-of-plane relative motion can be completely decoupled based on the new model. The inverse transformation of state transfer matrix is obtained to analyze perturbation effects and control strategy. The geometric characteristics of relative motion can be easily described using the relative eccentricity/inclination vector method. The proposed method and conclusions are validated by simulation through some typical examples. This paper improves the basic theory of relative orbit elements and unifies the expressions of the elliptical and near-circular close relative motion.     

航天器柔性多体系统动力学的高效建模方法

以航天器为工程背景,提出了一种高效建模方法。文中采用有限元离散和模态叠加法描述部件的弹性变形。用铰链相对坐标建立了相邻柔性体之间的递推运动学方程。利用递推运动学方程、柔性体的牛顿—欧拉方程和铰链的约束特性,构造了单链多体系统动力学问题的递推算法。对树状多体系统的拓扑结构进行了研究,提出了研究树状多体系统动力学问题的求解过程控制方法,从而实现了树状多体系统与链式多体系统的统一,使得对单链多体系统建立的递推动力学方程能够直接用于求解树状多体系统的动力学问题。     

Optimization of Multi-Orbit Transfers between Noncoplanar Elliptic Orbits

Using the maximum principle formalism, the problem of optimizing interorbital transfer between two noncoplanar elliptic orbits is reduced to solution of a boundary value problem for a system of ordinary differential equations. In order to solve the resulting boundary value problem numerically, the numerical homotopic method or modified Newton's method is used. When solving the boundary value problem, the right-hand sides of differential equations of motion are averaged numerically. Efficient software is developed, and a large number of optimal trajectories are calculated using it. As a result of analysis of these numerical data, new high-quality results are obtained. Specifically, a bifurcation of optimal solutions is found, the existence of critical inclination is demonstrated, and a partial classification of the structure of optimal control is performed.     

空间对接机构缓冲系统及其运动学建模

以异体同构周边式对接机构差动式缓冲系统为对象，将缓冲机构分解成6个独立分支，通过设计立局部坐标系，建立缓冲系统运动学正，逆解模型。该建模方法可以消除各分支之间的耦合关系，使建模得以简化。算例说明这种缓冲系统运动学模型是正确有效的。     

失效航天器姿态接管的SDRE微分博弈控制

针对燃料耗尽的失效航天器姿态接管控制问题,提出多颗微卫星协同实现姿态稳定的状态相关黎卡提方程(SDRE)微分博弈控制方法。首先,将姿态接管问题转化为多颗微卫星的微分博弈问题,基于组合航天器的姿态模型和微卫星的性能指标函数建立多颗微卫星的非线性微分博弈模型,微卫星通过独立优化各自的性能指标函数得到控制策略。其次,引入状态相关系数矩阵,将非线性博弈转化为状态相关线性二次型博弈,采用SDRE方法更方便地逼近微卫星的博弈均衡策略。最终通过李雅普诺夫迭代法求解耦合状态相关黎卡提方程组得到微卫星的状态反馈控制器,实现微卫星的自主决策。数值仿真验证了多颗微卫星采用微分博弈控制方法实现姿态接管的有效性和容错性。     

水击问题的Fourier谱方法计算

给出了推进剂供应系统管路内流体瞬变流动的数学模型,提出了采用Fourier谱方法求解瞬变流非线性偏微分方程的新方法。以一段两端分别连接贮箱和阀的直管道为例,利用该方法对阀门关闭后管道中形成的水击和压力振荡特性进行了求解,给出了相应的仿真结果,与已发表的采用特征线法和有限元法求解结果进行了比较。对数值计算中的非物理振荡问题进行了讨论。     

带多约束条件的次最优中制导律设计

针对使用捷联式导引头的制导弹药,设计了次最优中制导律,以满足卫星制导与激光制导两种模式的交接要求。由于涉及到时变系统的解析求解,一般情况下,带多约束条件最优制导律的设计非常困难。利用以下的方法来解决这一问题：首先根据最优控制理论确定次最优中制导律的结构框架,然后根据该框架反向推导出变参数的合理常数替代值。利用设计的次最优中制导律,在交接段,导引头量测视线偏差角远小于视场角,并考虑了控制能量和落地时脱靶量等方面的约束要求,具有非常简单的形式,仅较比例导引律多出一项,减少了制导指令计算对弹载计算资源的占用。     

An approach to the autoignition of a turbulent mixture

This paper considers the turbulent homogeneous mixing of two reactants undergoing a one step, second order, irreversible, exothermic chemical reaction with a rate constant of the Arrhenius type. A statistically stationary turbulent velocity field is assumed given and unaffected by mass or heat production due to the chemical reaction. Relative density fluctuations are neglected. A Hopf-like functional formalism is presented, with application to both statistically inhomogeneous and statistically homogeneous flows. Single and double point probability density function differential equations are derived from those functional equations. The limit of very large activation energies is considered; a low degree of statistical correlation between temperature and concentration fields during the ignition period is hypothesized. After making use of the homogeneity assumption a closure problem is still present due to the nonlocalness of the molecular diffusion term. The problem is rendered closed by assuming a Gaussian conditional expected value for the temperature at a point given the temperature at a neighboring point. The closure is seen to preserve very important mathematical and physical properties. A linear first order hyperbolic differential equation with variable coefficients for the probability density function of the temperature field is obtained. A second Damköhler number based on Taylor's microscale turns out to be an important controlling parameter. A numerical integration for different values of the second Damköhler number and the initial stochastic parameters is carried out. The mixture is seen to evolve towards an eventual thermal runaway, the detailed behavior however being different for different systems. Some peculiarities during the ignition period evolution are uncovered.     

变推力月球软着陆制导优化研究

提出了一种新的使用变推力火箭发动机实现月球定点软着陆制导的优化方法.在软着陆加速度抛物线(即二次函数)变化的条件下,通过一组代数方程连接初始条件和终端条件,避免了求解两点边值问题的迭代计算.给出了瞬时位置速度状态参数以及需要推力加速度、推力和秒流量的计算公式,并通过调整总飞行时间和着陆点位置实现了燃料消耗最小的优化处理.算例结果证明了这种方法的可行性和有效性.     

Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method

The problem of optimization of interplanetary trajectories is considered for spacecraft with a small-thrust ideally regulated engine. When the maximum principle is used, determination of the optimal trajectory is reduced to solution of a two-point boundary value problem for a system of ordinary differential equations. In order to solve this boundary value problem, the method of continuation in parameter is used, and with the help of it the formal reduction of the boundary value problem to a Cauchy problem is performed. Different variants of the continuation method are considered, including the method of continuation in the gravitational parameter which allows one to find extreme trajectories with a preset angular distance. The issues of numerical realization of the continuation method are discussed, and numerical examples of its use for solving the problems of optimization of interplanetary trajectories are presented.     

绳系空间太阳能电站动力学响应分析

利用绝对节点坐标方法研究绳系空间太阳能电站在轨飞行的太阳能电池板动力响应。通过勒让德变换引入广义动量,在约束哈密尔顿体系下建立轨道、姿态和弹性振动耦合的动力学方程。基于祖冲之类方法的思想,结合辛龙格-库塔方法对微分-代数方程进行数值求解。数值算例说明本文建模方法和数值算法都是有效的,能很好地保持系统约束和能量。最后分析了绳长、平台系统的质量、轨道高度对于梁中点挠度和轴向平均应变的影响。     

一种用于空间翻滚目标接近控制的相对运动建模方法

针对空间翻滚目标等一类相对运动复杂的接近控制问题，首先重点研究了基于微分几何理论的相对运动建模，建立视线旋转坐标系下的三维相对运动方程；然后将三维相对运动解耦为视线瞬时旋转平面内的相对运动和该平面的转动，建立了统一的控制器设计框架，形式统一简洁、物理意义明确，消除传统制导与控制策略中俯仰、偏航通道的耦合因素影响；最后通过六自由度仿真算例证明，相对运动模型物理意义明晰、鲁棒性强、控制精度高、工程实现容易。     

在中面载荷作用下正交各向异性矩形板后屈曲行为分析

本文利用摄动法和广义傅氏级数法分析了在中面载荷作用下正交各向异性矩形板后屈曲行为,对几种典型的纤维增强环氧复合材料矩形板后屈曲行为给出了结果,可供工程设计应用参考。     

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.