全球星摄动运动及摄动补偿运控策略研究

绕地卫星摄动运动是导致星座设计构型发散的主要因素,摄动补偿轨道控制是维持全     

空间太阳能电站姿态运动-结构振动耦合建模与分析

针对多旋转关节空间太阳能电站构型，利用基于能量等效原理的连续体等效方法将其等效为柔性梁模型，并考虑重力梯度影响，建立了姿态运动与结构振动的耦合动力学模型；结合Runge-Kutta 法和Newmark法的优点，提出了适用于求解姿态运动与结构振动耦合动力学方程的改进算法，相比于经典Runge-Kutta 法大幅提高了效率；利用改进算法得到了不同参数下的动力学响应。在此基础上，推导了结构振动量级随结构尺寸的六次方量级增加的规律，仿真结果表明尺寸过大引发不稳定现象；分析了姿态运动和重力梯度对结构振动频率和振幅的影响；发现了姿态运动周期受结构柔性影响而增大的现象，这种现象在低轨以及大初始姿态角下影响更为明显。     

Refinement of the Oblique Dipole Model in the Evolution of Rotary Motion of a Charged Body in the Geomagnetic Field

When solving problems related to the induction of the Earth's magnetic field, the potential of which is expressed in the form of a series of spherical harmonic functions, it is necessary to use an approximate model of the geomagnetic field that satisfies the two conflicting requirements of simplicity and accuracy. As is noted in [3, p. 10], at the stage of design of satellites, especially at the stage of preliminary analysis of their dynamics, simple models of the geomagnetic field are usually employed. This offers additional possibilities for theoretical analysis of the problem. The averaged model and the model of a right dipole are just such simple models. The quadrupole model of the geomagnetic field developed in [4] is more accurate, but also more complex. The model of an oblique or skewed dipole is intermediate. The quadrupole model generalizes the simpler models mentioned above, and its analysis allows estimation of the accuracy of each model. It turns out that the oblique dipole model, which differs from the model of a right dipole by small correcting terms, does not take into account other correcting terms caused by the quadrupole part of the geomagnetic field, which are greater in magnitude. The evolution of the rotary motion of a charged rigid body in the geomagnetic field is considered, and the incorrectness of the oblique dipole model is demonstrated. The effect of the quadrupole component of the geomagnetic field on the body dynamics is revealed.     

Uncontrolled Attitude Motion of the Orbital Station MIR in the Last Months of Its Flight

The results of determination of the uncontrolled attitude motion of the orbital station MIR on four prolonged segments of its unmanned flight in 2000 and 2001 are presented. The determination was carried out on the basis of the data of onboard measurements of the Earth's magnetic field. The data obtained on a time interval of several hours were processed jointly by the least squares method by integration of the equations of motion of the station with respect to its center of mass. The processing resulted in the estimation of the initial conditions of the motion and of the parameters of the mathematical model used. Several types of regular motion were observed on sufficiently prolonged time intervals on the studied segments. Some of these motions were planned; others were established spontaneously.     

飞船的双冲量最优交会

本文利用作者在文献中所介绍的Clohessy—Wiltshire方法,在线性引力模型的假设下,求得了实现双冲量交会的最优解析解,即实现交会所需施加的两次冲量之和最小。数字仿真表明,本分析是正确的。     

Individual differences in susceptibility to motion sickness among six Skylab astronauts

One of the Skylab experiments dealt with motion sickness, comparing susceptibility in the workshop aloft with susceptibility preflight and postflight. Tests were conducted on and after mission-day 8 (MD 8) by which time the astronauts were adapted to working conditions. Stressful accelerations were generated by requiring the astronauts, with eyes covered, to execute standardized head movements (front, back, left, and right) while in a chair that could be rotated at angular velocities up to 30 rpm. The selected endpoint was either 150 discrete head movements or a very mild level of motion sickness. In all rotation experiments aloft, the five astronauts tested (astronaut 1 did not participate) were virtually symptom free, thus demonstrating lower susceptibility aloft than in preflight and postflight tests on the ground when symptoms were always elicited. Inasmuch as the eyes were covered and the canalicular stimuli were the same aloft as on the ground, it would appear that lifting the stimulus to the otolith organs due to gravity was an important factor in reducing susceptibility to motion sickness even though the transient stimuli generated under the test conditions were substantial and abnormal in pattern. Some of the astronauts experienced motion sickness under operational conditions aloft or after splashdown, but attention is centered chiefly on symptoms manifested in zero gravity. None of the Skylab-II crew (astronauts 1 to 3) was motion sick aloft. Astronaut 6 of the Skylab-III crew (astronauts 4 to 6) experienced motion sickness within an hour after transition into orbit; this constitutes the earliest such diagnosis on record under orbital flight conditions. The eliciting stimuli were associated with head and body movements, and astronaut 6 obtained relief by avoiding such movements and by one dose of the drug combination 1-scopolamine 0.35 mg + d-amphetamine 5.0 mg. All three astronauts of Skylab-III experienced motion sickness in the workshop where astronaut 6 was most susceptible and astronaut 4, least susceptible. The higher susceptibility of SL-III crewmen in the workshop, as compared with SL-II crewmen, may be attributable to the fact that they were based in the command module less than one-third as long as SL-II crewmen. The unnatural movements, often resembling acrobatics, permitted in the open spaces of the workshop revealed the great potentialities in weightlessness for generating complex interactions of abnormal or unusual vestibular and visual stimuli. Symptoms were controlled by body restraint and by drugs, but high susceptibility to motion sickness persisted for 3 days and probably much longer; restoration was complete on MD 7. From the foregoing statements it is clear that on and after MD 8 the susceptibility of SL-II and SL-III crewmen to motion sickness under experimental conditions was indistinguishable. The role played by the acquisition of adaptation effects prior to MD 8 is less clear and is a subject to be discussed.     

Uncontrollable Rotational Motion of the Mir Orbital Station

The results of determining the rotational motion of the Mir orbital station are presented for four long segments of its unmanned uncontrolled flight in 1999–2000. The determination was carried out using the data of onboard measurements of the Earth's magnetic field intensity. These data, taken for a time interval of several hours, were jointly processed by the least squares method with the help of integration of the equations of station motion relative to its center of mass. As a result of this processing, the initial conditions of motion and the parameters of the mathematical model used were evaluated. The technique of processing is verified using the telemetry data on angular velocity of the station and its attitude parameters. Two types of motion were applied on the investigated segments. One of them (three segments) presents a rotation around the axis of the minimum moment of inertia. This axis executes small oscillations with respect to a normal to the orbit plane. Such a motion was used for the first time on domestic manned orbital complexes. The second type of motion begins with a biaxial rotation which, in a few weeks, goes over into a motion very similar to the rotation around the normal to the orbit plane, but around the axis of the maximum moment of inertia.     

Periodic motions of a nearly dynamically symmetric satellite in the neighborhood of hyperboloidal precession

The motion of a satellite close to a dynamically symmetric solid body in a Newtonian gravitational field over a circular orbit is studied. The system of differential equations describing the body’s motion is close to a system with cyclic coordinate. New classes of periodic motions are constructed in the neighborhood of a known partial solution to an unperturbed problem, hyperboloidal precession of a dynamically symmetric satellite. In the resonance case, when the ratio of one frequency of small oscillations of a reduced system with two degrees of freedom in the neighborhood of a stable equilibrium position to the frequency of cyclic coordinate variation is close to an integer number, there exist one or three families of periodic motions that are analytic in terms of fractional powers of a small parameter. A study of stability of these motions was performed with the help of KAM (Kolmogorov-Arnold-Moser) theoty. Faling the described resonance there exists a unique family of periodic motions that is analytic in terms of integer powers of a small parameter. The check-up of stability of these motrons was carried out. We distinguished the cases of parametric resonance, resonances of the third and fourth orders, and a non-resonant case. In the resonance cases our study relies on well-known results on stability of Hamiltonian systems during resonances [1]. In the non-resonant case we use the KAM theory [2].     

柔性绳网动力学建模与天地差异性分析

采用有限元模型研究了柔性绳网系统的动力学特性。针对空间绳网直接弹射展开方式,首先将绳网离散为若干单元,各单元处理为非线性“半阻尼弹簧”模型,然后分别计算各单元所受气动力和重力,最终建立绳网系统多柔体动力学模型。基于所建立的动力学模型分别对柔性绳网在地面和太空展开的动力学过程进行了仿真分析,研究了绳网在展开面积、空间位形和飞行距离等方面的天地差异性及其动力学机理,为未来空间绳网系统的分析设计提供理论参考。     

A hydrodynamic analogy of the solution to double-averaged Hill problem

A hydrodynamic analogy for the solution of doubly averaged Hill problem obtained by M.L. Lidov [1] is discussed. S.A. Chaplygin used a similar analogy reducing the two-dimensional problem of motion of a compressible fluid to the same problem for some fictitious incompressible fluid [2]. In this case, we are led to the range of ideas which go back to the work by N.E. Zhukowski [3]. Two versions of this hydrodynamic analogy, on the basis of the model of a stratified fluid (exact analogy) and on the basis of the model of a homogeneous fluid (approximate analogy), are considered as well as some consequences of them.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 126–134.Original Russian Text Copyright © 2005 by Rabinovich, Prokhorenko.     

Quaternion regularization in celestial mechanics and astrodynamics and trajectory motion control. I

Regularization problems in celestial mechanics and astrodynamics are considered. The fundamental regular quaternion models of celestial mechanics and astrodynamics are presented. It is shown that the efficiency of analytical investigation and numerical solution of boundary problems of optimal trajectory motion control of spacecraft may be increased using quaternion astrodynamics models. The regularization problem of celestial mechanics and astrodynamics that implies eliminating the feature, which arises in the equations of the two-body problem in case of impact of the second body with the central body, is considered in the first section of the paper. The quaternion method for regularizing the equations of the perturbed spatial two-body problem suggested by the author is presented; the method is compared with Kustaanheimo-Stiefel (KS) regularization. Demonstrative geometric and kinematic interpretations of regularizing transformations are provided. Regular quaternion equations for the two-body problem, which generalize the regular Kustaanheimo-Stiefel equations, as well as regular equations in quaternion osculating elements and quaternion regular equations for perturbed central motion of a material point, are considered. The papers on quaternion regularization in celestial mechanics and astrodynamics are briefly analyzed.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: III

The results of numerical solution of the problem of a rendezvous in the central Newtonian gravitational field of a controlled spacecraft with an uncontrollable spacecraft moving along an elliptic Keplerian orbit are presented. Two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems and using quaternion variables to describe the orientations of these coordinate systems. The problem of a rendezvous of two spacecraft is formulated [1, 2] as a problem of optimal control by the motion of the center of mass of a controlled spacecraft with a movable right end of the trajectory, and it is solved on the basis of Pontryagin's maximum principle. The paper is a continuation of papers [1, 2], where the problem of a rendezvous of two spacecraft has been considered theoretically using the two above variants of the equations of motion for the center of mass of the controlled spacecraft.     

Effect of gravity on the solidification of binary alloys—A numerical simulation

The paper illustrates the influence of gravity on convection in the mushy zone of solidifying alloys by numerical solution of the governing equations for the fluid flow.Different models for the permeability are compared and the effect of convection in the liquid ahead of the solidification front is taken into account.     

微重力环境中重力梯度加速度引起的流体晃动运动

本文研究了关于旋转轴在贮箱的非对称轴上且远离贮箱的几何中心情况下，流体在微重力环境中由重力梯度加速度诱发的晃动特性，建立了问题的数学模型并对模型进行了数值模拟。以高级Ｘ射线天文物理实验卫星（简称ＡＸＡＦ─Ｓ）作为研究对象，获得了由旋转运动引起的重力梯度加速度的数学表达式。晃动问题的数值计算以与卫星固连的非惯性坐标系为基础，目的是寻求一种较为易处理且适合于流体力学方程的边界和初始条件。通过数值计算获得了流体作用于卫星贮箱上的力和力矩。     

Uncontrolled Attitude Motion of the Foton-12 Satellite and Quasi-Steady Microaccelerations onboard It

The results of determination of the uncontrolled attitude motion of the Foton-12 satellite (placed in orbit on September 9, 1999, terminated its flight on September 24, 1999) are presented. The determination was carried out by the onboard measurement data of the Earth's magnetic field strength vector. Intervals with a duration of several hours were selected from data covering almost the entire flight. On each such interval the data were processed simultaneously using the least squares method by integrating the satellite's equations of motion with respect to the center of mass. The initial conditions of motion and the parameters of the mathematical model employed were estimated in processing. The results obtained provided for a complete representation of the satellite's motion during the flight. This motion, beginning with a small angular velocity, gradually sped up. The growth of the component of the angular velocity with respect to the longitudinal axis of the satellite was particularly strong. During the first several days of the flight this component increased virtually after every passage through the orbit's perigee. As the satellite's angular velocity increased, its motion became more and more similar to the regular Euler precession of an axisymmetric rigid body. In the last several days of flight the satellite's angular velocity with respect to its longitudinal axis was about 1 deg/s and the projection of the angular velocity onto the plane perpendicular to this axis had a magnitude of approximately 0.15 deg/s. The deviation of the longitudinal axis from the normal to the orbit plane did not exceed 60°. The knowledge of the attitude motion of the satellite allowed us to determine the quasi-steady microacceleration component onboard it at the locations of the technological and scientific equipment.     

Optimization of Low-Thrust Interplanetary Transfers

A method for approximate analytical optimization of low-thrust transfers, described in [1] and based on linearization of the equations of motion, is considered. A more precise method of reducing the errors due to linearization is suggested. The method of optimization is generalized for the case of a mission to several celestial bodies.     

Quaternion regularization and trajectory motion control in celestial mechanics and astrodynamics: II

Problems of regularization in celestial mechanics and astrodynamics are considered, and basic regular quaternion models for celestial mechanics and astrodynamics are presented. It is shown that the effectiveness of analytical studies and numerical solutions to boundary value problems of controlling the trajectory motion of spacecraft can be improved by using quaternion models of astrodynamics. In this second part of the paper, specific singularity-type features (division by zero) are considered. They result from using classical equations in angular variables (particularly in Euler variables) in celestial mechanics and astrodynamics and can be eliminated by using Euler (Rodrigues-Hamilton) parameters and Hamilton quaternions. Basic regular (in the above sense) quaternion models of celestial mechanics and astrodynamics are considered; these include equations of trajectory motion written in nonholonomic, orbital, and ideal moving trihedrals whose rotational motions are described by Euler parameters and quaternions of turn; and quaternion equations of instantaneous orbit orientation of a celestial body (spacecraft). New quaternion regular equations are derived for the perturbed three-dimensional two-body problem (spacecraft trajectory motion). These equations are constructed using ideal rectangular Hansen coordinates and quaternion variables, and they have additional advantages over those known for regular Kustaanheimo-Stiefel equations.     

An Analysis of the Low-Frequency Component in Measurements of Angular Velocity and Microacceleration onboard the Foton-12 Satellite

We compare the results of two methods used to determine the angular velocity of the Foton-12 satellite and the low-frequency component of microaccelerations onboard it. The first method is based on reconstruction of the satellite's rotational motion using the data of onboard measurements of the strength of the Earth's magnetic field. The motion (time dependence of the orientation parameters and angular velocity) was found from the condition of best approximation of the measurement data by the functions calculated along the solutions to equations of attitude motion of the satellite. The solutions found were used to calculate the quasistatic component of microaccelerations at certain points of the satellite, in particular, at the point of location of an accelerometer of the QSAM system. Filtration of the low-frequency component of the angular velocity and microacceleration from the data of measurements by a sensor of angular velocity and by the accelerometer of this system served as a second method. The filtration was made using the discrete Fourier series. A spectral analysis of the functions representing the results of determining the angular velocity and microacceleration by both methods is performed. Comparing the frequencies and amplitudes of the harmonic component of these functions allowed us to estimate the accuracy of measurements made by the QSAM system in the low-frequency range.     

基于不同动力引力辅助模型的木星转移轨道设计

针对木星转移轨道设计中动力引力辅助模型选择问题展开了研究。首先,介绍了近心点机动和甩摆后机动2种动力引力辅助模型,给出了2种模型下最优脉冲机动速度增量的解算方法;然后,基于动力引力辅助模型,提出了包含引力辅助的行星际转移轨迹初始设计方法;最后,以木星探测任务转移轨迹设计为例,对比了不同动力引力辅助模型下探测器的燃料消耗情况。仿真结果表明:相比于甩摆后机动方式,近心点轨道机动方式更加节省燃料。基于近心点机动引力辅助模型,最终完成了金星-地球-地球引力辅助序列的木星转移轨迹初始设计,为我国未来采用引力辅助方式的深空探测任务提供了一定的参考。