On the stability of spinning satellites

We study the directional stability of rigid and deformable spinning satellites in terms of two attitude angles. The linearized attitude motion of a free system about an assumed uniform-spin reference solution leads to a generic MGK system when the satellite is rigid or deformable. In terms of Lyapunov’s stability theory, we investigate the stability with respect to a subset of the variables. For a rigid body, the MGK system is 6-dimensional, i.e., 3 rotational and 3 translational variables. When flexible parts are present the system can have any arbitrary dimension. The 2×2 McIntyre–Myiagi stability matrix gives sufficient conditions for the attitude stability. A further development of this method has led to the Equivalent Rigid Body method. We propose an alternative practical method to establish sufficiency conditions for directional stability by using the Frobenius–Schur reduction formula. As practical applications we discuss a spinning satellite augmented with a spring–mass system and a rigid body appended with two cables and tip masses. In practice, the attitude stability must also be investigated when the spinning satellite is subject to a constant axial thrust. The generic format becomes MGKN as the thrust is a follower force. For a perfectly aligned thrust along the spin axis, Lyapunov’s indirect method remains valid also when deformable parts are present. We illustrate this case with an apogee motor burn in the presence of slag. When the thrust is not on the spin axis or not pointing parallel to the spin axis, the uniform-spin reference motion does not exist and none of the previous methods is applicable. In this case, the linearization may be performed about the initial state. Even when the linearized system has bounded solutions, the non-linear system can be unstable in general. We illustrate this situation by an instability that actually happened in-flight during a station-keeping maneuver of ESA’s GEOS-I satellite in 1979.     

Real Time Satellite Position Determination for TDMA Systems

A real time satellite position determination method using a single reference station is presented. The satellite position is determined from these three parameters: the distance between the reference station and the satellite that can be obtained by a single-hop measurement, the elevation angle, and the azimuth angle obtained from the antenna encoder. The error of the transmit frame delay is determined from the position equations, together with other possible errors. The accuracy is about ± 42 symbols for a 90 Mbit/s timedivision multiple access (TDMA) system using an encoder with a ± 0.001 ? resolution.     

关联大系统强稳定性的主要结果

综述了近十余年来关联大系统强稳定性的研究进展．指出了系统可靠性研究与强稳定性研究之间的关系，给出了强稳定性研究的主要结果以及强稳定性的各种定义方法．文中着重分析了强稳定方法的研究途径和主要不足方面，并探讨了强稳定性研究的发展趋势．     

Orbital and relative motion of a tethered satellite system

A simplified model for the orbital and relative motion of a tethered satellite system is presented. The tether acts as a light elastic string with small structural damping but without bending stiffness. Its mass is taken into account in the calculation of the total kinetic and potential energies of the tethered system. This formulation allows the inclusion of the complete gravity gradient influence on the dynamics of the system. The resulting three-dimensional motion is separated in the centre of mass orbital motion on the one hand and the relative motion of the end-bodies on the other. No restrictions on length of the tether or on mass ratio of the end-masses are imposed. It is found that the frequencies and amplitudes of the longitudinal tether oscillations are realistic as long as the tether mass is less than that of the subsatellite.     

Magnetically suspended MEMS spinning wheel gyro

A concept of a magnetically suspended spinning wheel gyro is described. The gyro is based on a patented, planar magnetic actuator and position sensor configuration with a gyro wheel that is rotated by a multi-phase electromagnetic spin motor. The motor and actuator/sensor configurations, in addition to providing the necessary forces to suspend the spinning wheel, are amenable to fabrication using some of the developing MEMS fabrication technologies, making batch fabrication of the gyro possible. This provide the capability for high production yield in high volume through the use of batch processing, without the need for skilled hand labor, resulting in high yields, high reliability, and low cost of ownership. The gyro concept is described in detail. The high-speed rotation of the wheel, somewhat smaller than a dime, can produce an angular momentum much larger than that of the Coriolis force based MEMS gyros now receiving intensive development, and is expected to provide considerably higher performance than currently available from this class of instrument. Two axes of angular rate information and three axes of acceleration information are provided by the control loops that center the wheel within the case. Thus, two such magnetically suspended spinning wheel gyros can be used to implement a complete IMU, and can also provide redundancy in three of the five degrees of freedom     

Design of a CLOS guidance law via feedback linearization

An application of the feedback linearization technique to the design of a new command to line-of-sight (CLOS) guidance law for short-range surface-to-air missiles is described. The key idea lies in converting the three-dimensional CLOS guidance problem to the tracking problem of a time-varying nonlinear system. The result may shed new light on the role of the feedforward acceleration terms used in the conventional CLOS guidance laws. Through computer simulation, the effect of the dynamics of the ground tracker and the autopilot on the guidance performance of the new CLOS guidance law is investigated     

Geostationary Satellite Navigation Systems

The concept of position determination using geostationary satellites as an alternative to the global positioning system (GPS) is studied. The advantage of a geostationary system is that only three, or at most four, satellites are required to cover the continental United States. A total of twelve satellites are sufficient for global coverage (excluding polar regions), or eight if only longitude and latitude, but not altitude, are measured. The system involves the determination of the range to either four geostationary satellites or, if the altitude is not measured, three geostationary satellites. The accuracy of the proposed systems are evaluated to obtain the rms error associated with position determination, and the concept for the implementation of measurements required by the systems is presented. The accuracy of the systems are adequate for civilian use in the continental United States; however, there is a degradation in accuracy as the location of the user approaches the equator.     

疲劳破坏寿命的概率统计方法研究综述

概述了结构疲劳破坏寿命特性概率统计方法研究的发展及理论基础，从常规疲劳特性P－S－N曲线的研究应用、疲劳裂纹扩展率统计模型研究现状以及损伤力学理论在疲劳强度中的研究展望来综述现有随机疲劳破坏寿命分布统计特性曲线的研究方法和工程应用，同时介绍该领域研究的新成果新方法，对疲劳破坏随机性研究的未来发展的关键及趋势提出看法。     

Time variations of the total electron content in the Southeast Asian equatorial ionization anomaly for the period 2006–2011

This study presents the time variations of the total electron content in the South East Asian equatorial ionization anomaly. The time variation of the TEC is analyzed through the period 2006–2011 by using a latitudinal chain of GPS stations extending in the northern and southern hemisphere. The data shows that the shape of the diurnal variation of the TEC depends on the latitude: a plateau is observed at the stations near the equator and a Gaussian at the station distant from the equator. We observe a semiannual pattern in all the stations with maxima at equinox. In both hemispheres, the amplitude of the crest is larger in spring than autumn from 2006 to 2008 and smaller in spring than in autumn from 2009 to 2011. We also observe an asymmetry between the amplitude and the position of the two crests of ionization. There is a very high level of correlation between the amplitude of the TEC at the two crests and the sunspot number: ∼0.88. During the deep solar minimum 2008–2009, the amplitude of crests of ionization becomes small during several months in summer and winter. The results show that both crests move significantly equatorward in winter than other seasons and there is a tendency for both crests to appear earlier in winter and later in summer.