飞行器角速度测量的三轴加速度计法

飞行器角速度的测量在航空航天领域是极为重要的问题,然而现在主流的利用陀螺仪测量角速度的方法有造价较高这一问题。本文提出了一种通过测量刚体上非共线三点的加速度得到刚体角速度的方法,可以利用极为廉价的高精度加速度计较为准确地测量高速稳态飞行器的角速度。本文应用刚体运动学中的基点法,得到由刚体上非共线三点的加速度和其距离表示的刚体角速度,并对其进行了误差分析。最终采用数值模拟的方法,分析了此方法在具有较高角速度的飞行器和具有较低角速度的稳态卫星上得到的角速度的适用性。模拟结果表明,此种方法适用于稳态高角速度的飞行器。     

封面故事

正刘晏铭等提出了通过测量飞行器上非共线三点的加速度得到飞行器角速度的方法,即利用廉价的高精度加速度测量高速稳态飞行器的角速度。图示场景为飞行器在轨服务过程中具有较高的稳态角速度,从而保持对地指向,即z轴方向始终指向地心。为了测量飞行器的稳态角速度,使用高精度加速计的方法能够替代传统的陀螺仪,     

刚体在固定面上纯滚时接触点的速度和加速度

 在微小的时间间隔内，应用加速度合成定理和刚体上一点的加速度公式，推导出了接触点的加速度公 式. 加速度方向为运动刚体表面在该处的法线方向，大小与动接触线和定接触线的曲率半径 和刚体运动的角速度有关. 利用接触点的运动性 质，不仅有助于解答圆球在固定圆球面或圆柱在固定圆柱面上的纯滚问题，而且为求解一般 形状刚体在任意固定曲面上的纯滚问题提供了方便.     

计算复合运动中刚体的角加速度和点加速度的矢量法

具有几个定轴转动刚体的复合运动,利用惯例的确定其时间矢量导数的方法计算刚体的角加速度和动点的加速度是极其困难的,为此,本文利用组合理论的矢量法进行简化计算,这个方法的优点是既易于列表解答又能保留其物理概念。     

一般运动刚体角速度向量引入的一种新方法

通过向量运算给出了角速度向量引入的一种较简单的方法. 利用刚体上的固连向量的导数与 其自身垂直的特点,得出反映刚体整体运动特性的角速度向量,并对这样的导出方法与刚体 角速度向量物理意义之间的联系进行了讨论.     

关于刚体角速度的认识与思考

从中学 就开始了解和学习角速度这个物理量. 认知也从中学的标量,到大学物理中的矢量.本文通过分析刚体一般运动时点的速度和加速度,证明了角速度是二阶张量,同时给出了角速度矢量表达需要满足的条件,明确指出角速度的准确表达必须用张量,角速度的简便表达可以用矢量. 最后讨论了几个与角速度相关的问题.     

平面运动刚体对加速度瞬心的动量矩方程及应用

设动系o'x'y'的原点为刚体上任一定点,动系相对于定系(惯性系)oxy作平动。刚体(简化成平面图形)的质心为C;某瞬时t图形上成为加速度瞬心的点为Q;图形上任一质点M_i其质量m_i,刚体总质量M;图形转动的角速度和角加速度为ω和ε;对加速...     

一种隐式结构MIMU设计及标度因数温度误差分析

高动态、恶劣温度环境的微型飞行器应用中,由温度引起的MIMU标度因数误差与结构安装误差的耦合问题非常突出,常规MIMU及其标度因数温度误差标定补偿方法不再适用。提出并设计了一种隐式结构MIMU,分析了温度对MIMU结构及标度因数的影响机理,建立了与温度二次项有关的MIMU角速度通道和加速度通道标度因数温度误差模型,并提出了“多温度点三方位正反速率和双方位正反角度”标定方法,解决了MIMU误差耦合问题。标定与补偿试验结果表明,隐式结构MIMU结构安装误差受温度影响非常小,而标度因数是与温度的二次项有关的;标度因数温度误差补偿后,MIMU角速度通道、加速度通道动态精度都得到了显著提高,验证了隐式结构MIMU设计及标定方法的有效性和优越性。     

刚体平面平行运动瞬时加速度中心的确定方法

 首先用解析法得到了求瞬时加速度中心的公式，并对其作了讨论；其次介绍了当刚体作 匀角速平面平行运动、变角速平面平行运动，且刚体上两点的加速度相互平行、相互垂直时 求瞬时加速度中心的几何作图法.     

一般运动刚体角速度向量引入的一种新方法

通过向量运算给出了角速度向量引入的一种较简单的方法.利用刚体上的固连向量的导数与其自身垂直的特点,得出反映刚体整体运动特性的角速度向量,并对这样的导出方法与刚体角速度向量物理意义之间的联系进行了讨论.     

基于修正型罗德里格斯参数的三维刚体摆姿态控制

3D 刚体摆是研究地球静止轨道航天器的一个力学简化模型, 它绕一个固定、无摩擦的支点旋转, 具有3 个转动自由度. 文章给出基于修正型罗德里格斯(Rodrigues) 参数描述的3D 刚体摆的姿态动力学方程, 针对3D 刚体摆姿态和角速度稳定的非线性控制设计问题, 基于无源性控制理论利用能量法设计了3D 刚体摆的系统控制器, 并证明了系统满足无源性. 构造了系统的李雅普诺夫(Lyapunov) 函数, 利用能量法设计出3D 刚体摆的姿态控制律, 并由拉萨尔(LaSalle) 不变集原理证明了该控制律的渐近稳定性. 仿真实验给出了3D 刚体摆在倒立平衡位置的姿态和角速度的渐近稳定性, 仿真实验结果表明基于能量方法的3D 刚体摆姿态控制是有效的.     

Analytical solutions for dynamics of dual-spin spacecraft and gyrostat-satellites under magnetic attitude control in omega-regimes

The attitude dynamics of a dual-spin spacecraft (a gyrostat with one rotor) with magnetic actuators attitude control is considered in the constant external magnetic field at the presence of the spacecraft’s own magnetic dipole moment, which is created proportionally to the angular velocity components (this motion regime can be called as “the omega-regime” or “the omega-maneuver”). The research of the dual-spin spacecraft angular motion under the action of the magnetic restoring torque is fulfilled in the generalized formulation close to the classical mechanics’ task of the heavy body/gyrostat motion in the Lagrange top. Analytical exact solutions of differential equations of the motion are obtained for all parameters in terms of elliptic integrals and the Jacobi functions. New obtained analytical solutions can be classified as results developing the classical fundamental problem of the rigid body and gyrostat motion around the fixed point. The technical application of the omega-regime to the angular reorientation of the spacecraft longitudinal axis along the angular momentum vector is considered.     

Optimal technology of inertial measurements

A technological project for measuring the spacecraft angular velocity vector is justified, the maximum accuracy is attained, and the proposed technology is compared with well-known methods for inertial measurements. The present paper is a continuation of [1].     

带空间机械臂航天器姿态运动规划的数值算法研究

自由漂浮空间机械臂系统在无外力矩作用时,系统的动量矩守恒而成为非完整系统。利用这一特性本文研究了自由漂浮空间机械臂系统的三维姿态运动规划问题。导出带空间机械臂的航天器三维姿态运动数学模型,将系统的非完整运动规划问题转化为非线性系统最优控制问题,在最优控制中利用小波逼近控制输入规律,提出基于遗传算法的最优控制数值算法。通过数值仿真,表明该方法对带空间机械臂航天器系统的非完整姿态运动规划是有效的。     

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.     

一种用于无陀螺捷联惯导系统的角速度融合算法

无陀螺捷联惯导系统(GFSINS)是用加速度计的合理空间组合解算出载体的角速度。载体角速度的解算精度是GFSINS的技术关键。在分析GFSINS九加速度计配置方案的基础上,提出一种新的角速度融合算法,消除该方案解算过程中开方计算及符号判断带来的误差。该算法还明显抵消了加速度计输出中包含的常值零点偏移误差和温度漂移误差等,具有实时性好、计算量小、通用性强的优点。仿真计算表明该算法可行,并能在一定程度上提高系统解算精度。     

Chaotic pitch motion of an asymmetric non-rigid spacecraft with viscous drag in circular orbit

We study the pitch motion dynamics of an asymmetric spacecraft in circular orbit under the influence of a gravity gradient torque. The spacecraft is perturbed by a small aerodynamic drag torque proportional to the angular velocity of the body about its mass center. We also suppose that one of the moments of inertia of the spacecraft is a periodic function of time. Under both perturbations, we show that the system exhibits a transient chaotic behavior by means of the Melnikov method. This method gives us an analytical criterion for heteroclinic chaos in terms of the system parameters which is numerically contrasted. We also show that some periodic orbits survive for perturbation small enough.     

Model predictive control of rigid spacecraft with two variable speed control moment gyroscopes

In this paper, an attitude maneuver control problem is investigated for a rigid spacecraft using an array of two variable speed control moment gyroscopes(VSCMGs)with gimbal axes skewed to each other. A mathematical model is constructed by taking the spacecraft and the gyroscopes together as an integrated system, with the coupling interaction between them considered. To overcome the singular issues of the VSCMGs due to the conventional torque-based method, the first-order derivative of gimbal rates and the second-order derivative of the rotor spinning velocity, instead of the gyroscope torques, are taken as input variables. Moreover, taking external disturbances into account,a feedback control law is designed for the system based on a method of nonlinear model predictive control(NMPC). The attitude maneuver can be realized fast and smoothly by using the proposed controller in this paper.     

Construction of optimal laws of variation in the angular momentum vector of a dynamically symmetric rigid body

We consider the problem of construction of optimal laws of variation in the angular momentum vector of a dynamically symmetric rigid body so as to ensure the transition of the rigid body from an arbitrary initial angular position to the required final angular position. For the functionals to be minimized, we use combined performance functionals, one of which characterizes the expenditure of time and of the squared modulus of the angular momentum vector in a given proportion, while the other characterizes the expenditure of time and momentum of the modulus of the angular momentum vector necessary to change the rigid body orientation. The control (the vector of the rigid body angular momentum) is assumed to be bounded in the modulus. The problem is solved by using Pontryagin’s maximum principle and the quaternion differential equation [1, 2] relating the vector of the dynamically symmetric rigid body angular momentum to the quaternion of orientation of the coordinate system rotating with respect to the rigid body about its dynamical symmetry axis at an angular velocity proportional to the angular momentum vector projection on the axis. The use of such a model of rotational motion leads to the problem of optimal control with the moving right end of the trajectory and significantly simplifies the analytic study of the problem of construction of optimal laws of variation in the angular momentum vector, because this model explicitly exploits the body angular momentum quaternion (control) instead of the rigid body absolute angular velocity quaternion. We construct general analytic solutions of the differential equations for the boundary-value problems which form systems of nine nonlinear differential equations. It is shown that the process of solving the differential boundary-value problems is reduced to solving two scalar algebraic transcendental equations.     

Passive deployment of a tether between two bodies in orbit

The authors consider the problem of deployment in orbit of a small tether that can serve as a standard of length for calibration of both onboard and ground optical and radar tracking systems, as an integrated sensor of the force fields of planets, etc. A tether for two bodies is examined. Possible methods for compact placement of a tether in orbit in operating condition are discussed. The main method is that of use of the centrifugal forces resulting from imparting to the tether an initial angular velocity in its deployment from the spacecraft. Various methods for creating moments of friction forces in hinges are considered. Numerical modeling of the dynamic processes is carried out within the framework of the theory of systems of bodies. Problems associated with determination of the required initial angular velocity and of the “cone of departure” of the tether from the spacecraft are examined. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 87–92, October, 1999.