挠性空间飞行器动力学

一、引言 随着空间事业的不断发展,空间飞行器的种类不断增多,其动力学结构也越来越复杂.其中绝大部份飞行器既不是单一的刚体,也不是单一的弹性体.带有大型太阳帆板的卫星就是其中的一个典型例子.     

基于欧拉角的分导飞行器多模型自适应姿态控制

基于欧拉角的变换得到了刚体飞行器的一种多模型自适应控制律,它能解决转动惯量不确定并随时发生突变的分导飞行器的姿态控制问题.该控制策略可以有效地检测出转动惯量发生突变,并及时切换到最合适的控制器.通过理论分析证明了该控制策略的闭环全局渐近稳定.数值仿真表明该方案的有效性.     

基于伴随同化方法的空间飞行器轨道估计

基于空间几何原理提出了一个双星无源定位方案,方案中包括两个观测坐标系和一个基础坐标系.每个观测坐标系中分别存在一条由观测卫星发出指向目标飞行器的射线,考虑到实际观测中存在各种误差,任意两颗观测卫星对目标飞行器的定位方向一般不在同一个平面内(即为异面直线),假定两条异面直线的公垂线段的中点(相交的情况下为交点)是目标飞行器所在的位置,而公垂线段的长度表征两颗卫星的观测误差.利用空间飞行器的观测数据计算了飞行器在基础坐标系中的位置坐标并进行了误差估计.利用一个基于伴随同化方法的数值模型估计了空间飞行器主动段的轨道.正向模型用来模拟飞行器的运动过程,伴随模型用来优化参数.通过同化空间飞行器在基础坐标系下的观测数据得到了空间飞行器的轨道.设计了数值实验以检验该模型的合理性,实验结果表明了双星无源定位系统的正确性,通过同化卫星对飞行器的观测数据,该伴随同化模型可以对空间飞行器的轨道进行成功估计.     

带弹性附件充液矩形贮箱俯仰运动动态响应

首先建立了俯仰运动矩形贮箱刚-液-弹耦合系统在外力矩作用下的耦合动力学模型,给出满足边界条件的速度势函数和液面波高的级数表达式,采用伽辽金法离散,将动力学模型转化为常微分方程组,得到刚-液-弹耦合系统的固有频率,给出简单的近似表达式,分析了转动中心距静液面不同位置时刚-液-弹耦合系统各阶固有频率的变化规律,系统转动中心距静液面较近时,耦合后液体反对称模态和刚体的固有频率对比耦合前减小,较远时则增大,最后进行数值验证,比较分析了液体和弹性体对刚体姿态的影响．     

具有确定运动姿势的柔性体的动力学分析研究

讨论了具有确定运动姿态的柔性多体系统的非线性动力学控制方程． 将飞行器在空间的运动看作是已知的,分析了飞行器上的挠性构件对飞行器运动和姿态的影响,利用假设模态,将挠性构件的变形,看作是空间直角坐标轴方向的线元振动所构成的,根据动力学中的Kane方法,建立了动力学方程,方程中包含表示弹性变形的结构刚度矩阵及表示变形体非线性变形几何刚度矩阵,方程推导从应力-应变关系入手,使用了有限元法．经简化,得到了带帆板结构的平面挠性体对飞行器运动影响的动力学方程,这种方程可通过计算机实现其数值解．     

超声速流场中6自由度物体运动的模拟研究

物体在流场中自由运动的模拟有很广泛的应用,文章描述计算6自由度(6DOF)刚体在超声速流场中自由运动的一种方法.流体部分求解LES方程,亚网格模型为拉伸涡模型.激波和刚体边界周围区域采用迎风型WENO格式,湍流区域采用低数值耗散的TCD格式.时间推进采用三阶的SSP R-K法.刚体采用6自由度模型,刚体姿态用四元数来表示,控制方程为常微分方程,采用四阶Runge-Kutta法求解.文章给出若干算例来验证程序的有效性,结果理想.     

空间飞行器轨道估计与误差分析

卫星探测是当今空间飞行器观测与轨道估计的重要方式.针对空间飞行器轨道估计及卫星无源探测的误差分析等问题,在双星观测条件下,使用样条插值及拟合的方法对包含随机误差和系统误差的初始数据进行光滑处理,然后基于立体几何和逐点交汇的思想建立了运动方程参数模型,采用最小二乘法估计参数,得到了空间飞行器的估计轨道,并使用LMF法进行了系统误差分析.针对单星观测的情况,一方面,认为飞行器轨道上的点共面且均在过地心的平面内,另一方面,通过建立飞行器轨道模版数据库与观测相对比,了解识别是何种飞行器.添加了这些约束和先验信息后,可以得到大致的轨道估计.     

以四面体为基础的组合单元的实用分析技巧

用有限单元法对弹性力学空间问题进行应力分析,首先必须将空间弹性体划分单元,这项工作往往带来很大的困难,特别是将空间弹性体划分为一系列四面体单元,这不仅需要很强的空间想象力,而且需要处理和输入数以万计的数据,这些据数进入内存后又耗费了大量的工作单元,影响计算机的解题范围.     

弹性问题单元构造中空间M_3(K)维数计算

<正>1引言线弹性方程的解空间是具有对称性质的应力矩阵和位移向量.在Hellinger-Reissner变分形式下,构造稳定的单元是有限元求解弹性问题的关键.其中,通过构造复合单元的方法[1,2,3,4,5]求解弹性问题,这种方法比较复杂.也可以通过用Lagrange乘子重建弹性问题的混合变分形式,对应力空间施加弱对称性,解决线弹性问题[6,7,8,9,10].2002年,Arnold和Winther在[11]构造了一系列稳定的协调三角形单元和刚体运动下的低     

基于卫星无源探测的空间飞行器主动段轨道估计与误差分析

在利用自适应定点的四阶龙格库塔算法求解卫星二阶微分运动方程的基础上,确定了其轨道,在利用样条插值拟合算法对多星观测数据同步后,基于级数理论建立了飞行器速速度和质量估计的多项式模型.随后根据飞行器在观测坐标系下的约束关系,建立了双星无源交汇定位的算法模型,实现了空间飞行器的轨道估计.再次,根据量测方程,提出了一种系统误差估计的滑窗四点交汇方法,实现了系统的误差动态估计.最后,建立了联合序贯多点轨道估计模型,实现了单卫星单飞行器的轨道估计和误差分析.对于多星多飞行器问题通过比较方程组自由度和待估计的轨道参数和系统误差的个数,得出可估计系统误差的条件:在观测卫星个数M与空间飞行器数目P满足2MP≥3P+2M时,系统误差可估计.     

Mathematical modelling and dynamic response of a multi-straight-line path tracing flexible robot manipulator with rotating-prismatic joint

In this study, mathematical modelling and dynamic response of a flexible robot manipulator with rotating-prismatic joint are investigated. The tip end of the flexible robot manipulator traces a multi-straight-line path under the action of an external driving torque and an axial force. Considered robot manipulator consists of a rotating prismatic joint and a sliding flexible arm with a tip mass. Flexible arm is assumed to be an Euler–Bernoulli beam carrying an end-mass. Equations of motion of the flexible manipulator are obtained by using Lagrange’s equation of motion. Effect of rotary inertia, axial shortening and gravitation is considered in the analysis. Equations of motion are solved by using fourth order Runge–Kutta method. Numerical simulations obtained by using a developed computer program are presented and physical trend of the results are discussed.     

Global mode method for dynamic modeling of a flexible-link flexible-joint manipulator with tip mass

In this paper, the global mode method (GMM) is proposed to obtain a reduced-order analytical dynamic model for a signal flexible-link flexible-joint (SFF) manipulator. Firstly, the nonlinear partial differential equations (PDE) that govern the motion of the flexible link and flexible joint, respectively, are derived by applying the Hamilton principle. By combining the linearized governing equations of motion for a flexible link and the equation of motion for the flexible joint, the characteristic equation is obtained for the whole system. The natural frequencies and global mode shapes of the linearized model of the SFF manipulator are determined, and orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to truncate the nonlinear PDEs of the SFF manipulator to a nonlinear ordinary differential equation with a few degrees-of-freedom (DOF). For comparison, two other dynamic models of the SFF are derived by employing the assumed mode method (AMM) and finite element method (FEM). To verify the method proposed, the results from the GMM are compared with those obtained from the FEM. The effects of the link length and payload mass on the convergence of AMM model for the first two frequencies are investigated. Based on the dynamic models, obtained by GMM and AMM, dynamical responses for the system with different numbers of modes are worked out numerically, which are compared with those obtained from FEM. These comparisons show a good agreement between the results of the GMM and that of the FEM model, which indeed proved the accuracy and applicability of the GMM model.     

Boundary layer analysis for the eigenvalues of hanging rod

The motion of a naturally straight inextensible flexible elastic hanging rod is formulated and then linearized about the straight solution. To solve this equation by separation of variables, an eigenvalue problem is derived. When the stiffness of the rod is small, the eigenvalue equation is a singular perturbation problem. This paper is devoted to solving this eigenvalue problem by boundary layer analysis when the stiffness is suitably small, especially on the analytic approximate solutions of the first several eigenvalues and eigenfunctions. The first three eigenvalues are also compared with the numerical results computed by a finite difference method. The excellent agreement shows the efficiency of the boundary layer analysis.     

Haar wavelet method for solving Fisher’s equation

In this paper, we develop an accurate and efficient Haar wavelet solution of Fisher’s equation, a prototypical reaction-diffusion equation. The solutions of Fisher’s equation are characterized by propagating fronts that can be very steep for large values of the reaction rate coefficient. There is an ongoing effort to better adapt Haar wavelet methods to the solution of differential equations with solutions that resemble shock waves or fronts typical of hyperbolic partial differential equations. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.     

A finite element technique for tape-head interaction problems in high-speed recording: The steady-state case

This paper presents a finite element technique to model the steady-state response of a flexible tape during high-speed recording. The tape is modeled as a flexible plate, including geometric nonlinearities due to large deflections. The air-film pressure field is described by using a modified version of the Reynolds equation for compressible fluids. A new nonlinear finite element that couples both air-film and tape mechanics is described in detail. This element, which has been incorporated into a standard finite element code (MSC/NASTRAN®), allows one to determine the pressure field and the air-film thickness due to tape-head interaction. An example demonstrates the usefulness of this technique.     

A qualitative analysis of the subharmonic oscillations of a parametrically excited flexible rod

A non-autonomous non-linear dynamical system with a small parameter that describes the parametric oscillations of a flexible rod with three static equilibrium positions is obtained. The generating equation of this model is a dynamical system in a plane with a separatrix loop. The qualitative analysis presented includes an investigation of the stability and bifurcation of subharmonic motions at resonance energy levels.     

Influence of mass moment of inertia on the normal modes of a preloaded solar array mast

Earth-orbiting spacecraft often contain solar arrays or antennas supported by a preloaded mast. Due to weight and cost considerations, the supporting structures of the spacecraft appendages are made extremely light and flexible. Therefore, it is essential to investigate the influence of all physical and structural parameters on the dynamic behavior of the overall structure. The governing equation of motion and its general solution for the preloaded mast are developed. Furthermore, the mass moment of inertia of the mast subjected to bending vibrations is included in the governing equation of motion to investigate its influence on determining the circular frequencies. To verify the developed formulations, a finite element technique was implemented. The accuracy and limitation of the technique on calculating the circular frequencies are discussed. Although the study described in this paper primarily focuses on the mast for the space station solar arrays, the developed formulations and techniques can be applied to any large and flexible beam in zero gravity.     

ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS

In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.     

THE LIE ALGEBRA ADMITTED BY ANORDINARY DIFFERENTIAL EQUATION SYSTEM

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