Asymmetric wedging of elastic material with the formation of separation zones

The problem of asymmetrical movement of a thin rigid impactor in elastic material is considered with subsonic and transonic velocities. For all considered range of velocities the flow diagram was determined for contours in the forms of wedge and ogive. There is a limiting speed value when the impactor moves with velocity higher than the speed of transverse wave at which the separation zone in the nasal part of the body disappears. At this velocity forces acting on the impactor are independent of its shape.     

旋转充液系统全飞行过程非线性动力学仿真

本文考虑一类刚认耦合的旋转充液系统的飞行动力学问题，在依据力学变分原理给出基本方程，导出全飞行过程运动状态方程的基础上，建立了相应的仿真模型。可能通过对Navier-Stokes方程求解和液体流动的惯性波振动特性，给出液体的反作用力矩。经过仿真实验，分析角运动的时间序列，给出了比较详尽的飞行不稳定机制分析结果。     

A study of angular motion of the Chibis-M microsatellite with three-axis flywheel control

We study the controlled angular motion of the Chibis-M microsatellite. Executive elements are three pairs of flywheels, whose axes are mutually perpendicular. The task of the control system is realization of a required program motion and support of its asymptotic stability. In this paper, we synthesize a control algorithm and study the evolution of the angular momentum of flywheels on long time intervals. The attitude accuracy is estimated for the case when disturbances act upon the spacecraft.     

Rapid rotations of a satellite with a cavity filled with viscous fluid under the action of moments of gravity and light pressure forces

Rapid rotational motion of a dynamically asymmetric satellite relative to the center of mass is studied. The satellite has a cavity filled with viscous fluid at low Reynolds numbers, and it moves under the action of moments of gravity and light pressure forces. Orbital motions with an arbitrary eccentricity are supposed to be specified. The system, obtained after averaging over the Euler-Poinsot motion and applying the modified averaging method, is analyzed. The numerical analysis in the general case is performed, and the analytical study in the axial rotation vicinity is carried out. The motion in the specific case of a dynamically symmetric satellite is considered.     

摇摆条件下惯性平台系统动态特性分析

惯性平台系统可以隔离角运动的技术特点为惯性仪表提供了良好的工作环境,但是轴端摩擦力矩的存在,将导致基座的摇摆运动对平台台体的稳定性产生影响,引起台体各轴的附加常值漂移即平台摇摆漂移。对于摇摆漂移的产生机理,国内外主要集中分析了运动学耦合原因。本文根据平台系统的稳定工作原理,首次通过建立平台系统的动力学方程,详细分析了摇摆条件下平台的动态特性,从平台动力学的角度详细分析了产生摇摆漂移的机理。结果表明,被稳定的台体各轴的运动特性是绕各轴摩擦力矩以及其余两轴角运动等导致的综合运动,既有单纯的跟踪运动,也有复杂的耦合运动,只有沿陀螺仪自转轴存在角运动,同时存在陀螺仪浮子转角的情况下,才有可能产生台体的摇摆漂移。     

Study of the mode of angular velocity damping for a spacecraft at non-standard situation

Non-standard situation on a spacecraft (Earth’s satellite) is considered, when there are no measurements of the spacecraft’s angular velocity component relative to one of its body axes. Angular velocity measurements are used in controlling spacecraft’s attitude motion by means of flywheels. The arising problem is to study the operation of standard control algorithms in the absence of some necessary measurements. In this work this problem is solved for the algorithm ensuring the damping of spacecraft’s angular velocity. Such a damping is shown to be possible not for all initial conditions of motion. In the general case one of two possible final modes is realized, each described by stable steady-state solutions of the equations of motion. In one of them, the spacecraft’s angular velocity component relative to the axis, for which the measurements are absent, is nonzero. The estimates of the regions of attraction are obtained for these steady-state solutions by numerical calculations. A simple technique is suggested that allows one to eliminate the initial conditions of the angular velocity damping mode from the attraction region of an undesirable solution. Several realizations of this mode that have taken place are reconstructed. This reconstruction was carried out using approximations of telemetry values of the angular velocity components and the total angular momentum of flywheels, obtained at the non-standard situation, by solutions of the equations of spacecraft’s rotational motion.     

Gravity-oriented satellite dynamics subject to gravitational and active damping torques

The dynamics of the rotational motion of a satellite moving in the central Newtonian field of force over a circular orbit under the effect of gravitational and active damping torques, which depend on the satellite angular velocity projections, has been investigated. The paper proposes a method of determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of damping coefficients and principal central moments of inertia. The conditions of their existence have been obtained. For a zero equilibrium position where the axes of the satellite-centered coordinate system coincide with the axes of the orbital coordinate system, the necessary and sufficient conditions for asymptotic stability are obtained using the Routh–Hurwitz criterion. A detailed analysis of the regions where the conditions of the asymptotic stability of a zero equilibrium position are fulfilled have been obtained depending on three dimensionless parameters of the problem, and the numerical study of the process of attenuation of satellite’s spatial oscillations for various damping coefficients has been carried out. It has been shown that there is a wide range of damping parameters from which, by choosing the necessary values, one can provide the asymptotic stability of satellite’s zero equilibrium position in the orbital coordinate system.     

The use of a movable telescoping end mass system for the time-optimal control of spinning spacecraft

The time-optimal control of a spin-stabilized spacecraft with a movable telescoping appendage (boom), is considered analytically and numerically. The motion of a control mass at the end of the boom is determined such that the terminal time will be minimized for two-axis control of a symmetric spacecraft. The equations of rotational motion are linearized about the desired state of spin about the symmetry axis. The equations for the transverse angular velocity components have the form of a coupled two dimensional harmonic oscillator with boom motion as a control force. The control function which brings the system to the desired state is known to be a series of positive and negative pulses. If the initial state is such that the system can be driven to rest in a single switch, the responses, switching and final times, and required boom motion may be determined analytically. Some typical numerical results based on these solutions are discussed.     

旋成体在无侧滑大攻角下的横向气动力特性

介绍具有尖锥头部细长旋成体（以下简称弹体）在无侧滑下横向气动力随攻角变化特性，其中包括尖锥头部顶角、旋成体长细比、初始滚转角、试验雷诺数诸参数对横向气动特性的影响。还介绍美国ＮＡＳＡ的一篇综合研究报告的部分结果。试验结果表明，在低亚音速下，弹体气动特性对上述诸参数反应极为敏感，有时呈现随机特性。头部加边条、减小长细比或在后体装尾翼，将有助于减弱横向气动力。采用弹体旋转飞行技术，虽然产生Ｍａｇｎｕｓ侧向力，但有效地克服了气动力的随机性。     

Informational approaches to angular motion control of spacecraft

Any information concepts may be used for motion control with respect to the center of masses of a reusable transport spacecraft (RTS). Using comparative analysis of the two concepts (the first one, based upon information about attitude parameters with respect to the inertial reference system and the second one, based upon parameters of angular motion with respect to wind-body coordinate system) for specific features of RTS dynamics and control at the stages of orbital flight, atmospheric flight under gas dynamic and aerodynamic control, and landing, paper demonstrates that information on angles of attack, slip and speed roll should be used for angular motion control at this stage of flight.     

基于输出反馈的编队卫星姿态同步和跟踪控制

研究了卫星编队无角速度测量信息且采用局部信息交互时的姿态协同控制问题.以四元数为姿态描述手段,采用超前滤波方法重构星体绝对和相对角速度信息,设计了基于输出反馈的分散姿态同步和跟踪控制器.利用Barbalat引理和代数图论等对闭环系统的全局渐近稳定性进行了理论分析和证明.以六星编队为背景的数值仿真进一步验证了算法的有效性.     

A two-dimensional approach to multibody free dynamics in space environment

The equation of motion of a multibody system, described here as a chain of rigid bars and revolute joints orbiting around the Earth, is derived.

For each bar two translational and one rotational equilibrium equations are written. The forces acting on each body are the gravitational forces and the reaction forces (unknown) acting on it's end joints. The complete set of equilibrium equations consists of N_X differential equations, where N_X is the order of the state vector. The total number of unknowns is N_X+N_R where N_R=2N_J and N_J is the number of joints. The N_R additional equations, to make the system determinate, are provided by the nondifferential compatibility equations.

The resulting system is a set of differential algebraic equations (DAE) for which the well-known method of reducing the system to ordinary differential equations (ODE) is applied.

Since the internal forces are associated with the relative displacements between the bodies, which are small fractions of the distance of the multibody spacecraft from the center of the Earth, the task of obtaining these forces from inertial coordinates, from a numerical viewpoint, could be impossible. So the problem is reformulated in such a way that the equation of motion of the system, contains global quantities where no internal forces appear, and local equations where internal forces do appear. In the latter one, only quantities of the same order of the spacecraft dimensions are present. Numerical results complete the work.     

Spin-stabilized satellite magnetic attitude control scheme without initial detumbling

The angular motion of an axisymmetrical satellite equipped with an active magnetic attitude control system is considered. The dynamics of the satellite are analytically studied on the whole control loop. The control loop is as follows: preliminary reorientation along with nutation damping, spinning about the axis of symmetry, then precise reorientation of the axis of symmetry in inertial space. Reorientation starts right after separation from the launch vehicle. Active magnetic attitude control system time-response with respect to its parameters is analyzed. It is proven that low-inclined orbit forces low control system time-response. Comparison with the common control scheme shows the time-response gain. Numerical analysis of the disturbances effect is carried out and good pointing accuracy is proved.     

Static-and-dynamic analysis of thin-walled structural members of space radio telescopes

Structural members of space radio telescopes made as large thin shells of revolution are analyzed. A twisting shell structure prestressed by inertia or surface-distributed forces (when in the unperturbed state) is used as the basis for the analysis. Loads due to solar wind, tides, control moments and nonuniform solar heating of the structure are considered as perturbations.A procedure for defining internal forces and moments and a varied structural geometry due to interaction of unperturbed and perturbed forces is given. The results of determining the frequencies of natural oscillations of the structure are also presented. Calculations are made on the basis of the obtained linearized equations reduced to quasi-univariate ones. A matrix factorization procedure allowing for constructing a stable-state numerical algorithm for solving the problem is employed.     

Asymptotic study of a complete magnetic attitude control cycle providing a single-axis orientation

The angular motion of an axisymmetrical satellite equipped with the active magnetic attitude control system is examined. Attitude control system has to ensure necessary orientation of the axis of symmetry in the inertial space. It implements the following strategy: coarse reorientation of the axis of symmetry with nutation damping or “-Bdot” without initial detumbling; spinning-up about the axis of symmetry to achieve the property of a gyro; fine reorientation of the axis in the inertial space. Dynamics of the satellite is analytically studied using averaging technique on the complete control loop consisting of five algorithms. Solutions of the equations of motion are obtained in terms of quadratures for most cases or even in closed-form. The latter allowed to study the dependence of motion parameters including time-response with respect to the orbit inclination and other parameters for all algorithms.     

Rotational motion of <Emphasis Type="Italic">Foton M-4</Emphasis>

The actual controlled rotational motion of the Foton M-4 satellite is reconstructed for the mode of single-axis solar orientation. The reconstruction was carried out using data of onboard measurements of vectors of angular velocity and the strength of the Earth’s magnetic field. The reconstruction method is based on the reconstruction of the kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected at a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are substituted in kinematic differential equations for a quaternion that defines the transition from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the satellite rotational motion. A solution of these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of the Earth’s magnetic field and its calculated values. The described method makes it possible to reconstruct the actual rotational satellite motion using one solution of kinematic equations over time intervals longer than 10 h. The found reconstructions have been used to calculate the residual microaccelerations.     

Biaxial Mode of Rotation of a Satellite in the Orbit Plane

A mode of motion of a satellite with respect to its center of mass is studied, which is called the biaxial rotation in the orbit plane. In this mode of rotation, an elongated and nearly dynamically symmetric satellite rotates around the longitudinal axis, which, in turn, rotates around the normal to the plane of an orbit; the angular velocity of rotation around the longitudinal axis is several times larger than the orbital angular velocity, deviations of this axis from the orbit plane are small. Such a rotation is convenient in the case when it is required to secure a sufficiently uniform illumination of the satellite's surface by the Sun at a comparatively small angular velocity of the satellite. The investigation consists of the numerical integration of equations of the satellite's motion, which take into account gravitational and restoring aerodynamic moments, as well as the evolution of the orbit. At high orbits, the mode of the biaxial rotation is conserved for an appreciable length of time, and at low orbits it is destroyed due to the impact of the aerodynamic moment. The orbit altitudes and the method of constructing the initial conditions of motion that guarantee a sufficiently prolonged period of existence of this mode are specified.     

Analysis of evolution of multi-orbit perturbed trajectories of a spacecraft in a central field of attraction

Properties of differential equations of multi-orbit trajectory motion of a spacecraft are investigated analytically. The spacecraft moves under the action of small perturbations (in particular, low thrust) in the plane of a central Newtonian field of attraction. The conditions are specified for existence of a partial singular aperiodic solution, in the neighborhood of which the behavior of osculating elements changes sharply. In this case, phase variables (the angular position of the pericenter and the true anomaly) are found to undergo the sharpest changes. The exact superposition of solutions is suggested for the equations of motion transformed to the form of a quasi-linear, weakly non-stationary system: a partial singular aperiodic solution and fast solutions oscillating around it. Asymptotic representations are obtained for both components of the superposition. They are fairly exact in the region of smallness of perturbing terms at a long variation of the argument.     

On stability of a rotating spacecraft partially filled with liquid: The case of a single cavity

The problem of stability of a rotating spacecraft with a cavity partially filled with liquid to a small depth is considered with regard to the distinction in angular velocities of spacecraft and liquid rotation and their variability (the modes of the spacecraft’s stationary rotation, spin-up, and rotation deceleration). The regions of stability (in space of the characteristic parameters of an object) are found, and mathematical simulating of the disturbed motion is carried out.     

基于角速率和速度增量的捷联惯性导航算法研究

捷联惯性导航算法一般是基于惯性器件输出为角速率、比力或角增量、速度增量进行设计的,不能直接应用于陀螺输出为角速率、加速度计输出为速度增量的捷联惯性导航系统。为了解决此问题和满足精度要求,重新设计了一套捷联惯性导航算法:姿态更新算法采用了经典的四阶龙格-库塔法,推导出了一种新的速度更新算法,该算法可以有效补偿速度计算中的划桨效应误差。仿真结果表明,该种速度更新算法仿真速度快、精度高,具有一定的工程实用价值。