一类边传递图

令G=（α,β｜α^n=β^2=1,α^β=α^r）,r＆^2≡1（modn），是图Г的一个自同构群。目的是研究关于G一边传递图的性质．运用置换群和代数图论的相关理论，获得了这类图的完全分类，它们是一些互不相交的圈和完全二部图的并。     

IDS contribution to ITRF2008

For the first time, the International DORIS Service (IDS) has produced a technique level combination based on the contributions of seven analysis centers (ACs), including the European Space Operations Center (ESOC), Geodetic Observatory Pecny (GOP), Geoscience Australia (GAU), the NASA Goddard Space Flight Center (GSFC), the Institut Géographique National (IGN), the Institute of Astronomy, Russian Academy of Sciences (INASAN, named as INA), and CNES/CLS (named as LCA). The ACs used five different software packages to process the DORIS data from 1992 to 2008, including NAPEOS (ESA), Bernese (GOP), GEODYN (GAU, GSC), GIPSY/OASIS (INA), and GINS (LCA). The data from seven DORIS satellites, TOPEX/Poseidon, SPOT-2, SPOT-3, SPOT-4, SPOT-5, Envisat and Jason-1 were processed and all the analysis centers produced weekly SINEX files in either variance–covariance or normal equation format. The processing by the analysis centers used the latest GRACE-derived gravity models, forward modelling of atmospheric gravity, updates to the radiation pressure modelling to improve the DORIS geocenter solutions, denser parameterization of empirically determined drag coefficients to improve station and EOP solutions, especially near the solar maximum in 2001–2002, updated troposphere mapping functions, and an ITRF2005-derived station set for orbit determination, DPOD2005. The CATREF software was used to process the weekly AC solutions, and produce three iterations of an IDS global weekly combination. Between the development of the initial solution IDS-1, and the final solution, IDS-3, the ACs improved their analysis strategies and submitted updated solutions to eliminate troposphere-derived biases in the solution scale, to reduce drag-related degradations in station positioning, and to refine the estimation strategy to improve the combination geocenter solution. An analysis of the frequency content of the individual AC geocenter and scale solutions was used as the basis to define the scale and geocenter of the IDS-3 combination. The final IDS-3 combination has an internal position consistency (WRMS) that is 15 to 20 mm before 2002 and 8 to 10 mm after 2002, when 4 or 5 satellites contribute to the weekly solutions. The final IDS-3 combination includes solutions for 130 DORIS stations on 67 different sites of which 35 have occupations over 16 years (1993.0–2009.0). The EOPs from the IDS-3 combination were compared with the IERS 05 C04 time series and the RMS agreement was 0.24 mas and 0.35 mas for the X and Y components of polar motion. The comparison to ITRF2005 in station position shows an agreement of 6 to 8 mm RMS in horizontal and 10.3 mm in height. The RMS comparison to ITRF2005 in station velocity is at 1.8 mm/year on the East component, to 1.2 mm/year in North component and 1.6 mm/year in height.     

DORIS geodesy: A dynamic determination of geocentre location

Geoscience Australia contributed a multi-satellite, multi-year weekly time series to the International DORIS Service combined submission for the construction of International Terrestrial Reference Frame 2008 (ITRF2008). This contributing solution was extended to a study of the capability of DORIS to dynamically estimate the variation in the geocentre location. Two solutions, comprising different constraint configurations of the tracking network, were undertaken. The respective DORIS satellite orbit solutions (SPOT-2, SPOT-4, SPOT-5 and Envisat) were verified and validated by comparison with those produced at the Goddard Space Flight Center (GSFC), DORIS Analysis Centre, for computational consistency and standards. In addition, in the case of Envisat, the trajectories from the GA determined SLR and DORIS orbits were compared. The results for weekly dynamic geocentre estimates from the two constraint configurations were benchmarked against the geometric geocentre estimates from the IDS-2 combined solution. This established that DORIS is capable of determining the dynamic geocentre variation by estimating the degree one spherical harmonic coefficients of the Earth’s gravity potential. It was established that constrained configurations produced similar results for the geocentre location and consequently similar annual amplitudes. For the minimally constrained configuration Greenbelt–Kitab, the mean of the uncertainties of the geocentre location were 2.3, 2.3 and 7.6 mm and RMS of the mean uncertainties were 1.9, 1.2 and 3.5 mm for the X, Y and Z components, respectively. For GA_IDS-2_Datum constrained configuration, the mean of the uncertainties of the geocentre location were 1.7, 1.7 and 6.2 mm and RMS of the mean uncertainties were 0.9, 0.7 and 2.9 mm for the X, Y and Z components, respectively. The mean of the differences of the two DORIS dynamic geocentre solutions with respect to the IDS-2 combination were 1.6, 4.0 and 5.1 mm with an RMS of the mean 21.2, 14.0 and 31.5 mm for the Greenbelt–Kitab configuration and 4.1, 3.9 and 4.3 mm with an RMS 8.1, 9.0 and 28.6 mm for the GA_IDS-2_Datum constraint configuration. The annual amplitudes for each component were estimated to be 5.3, 10.8 and 11.0 mm for the Greenbelt–Kitab configuration and 5.3, 9.3 and 9.4 mm for the GA_IDS-2_Datum constraint configuration. The two DORIS determined dynamic geocentre solutions were compared to the SLR determined dynamic solution (which was determined from the same process of the GA contribution to the ITRF2008 ILRS combination) gave mean differences of 3.3, −4.7 and 2.5 mm with an RMS of 20.7, 17.5 and 28.0 mm for the X, Y and Z components, respectively for the Greenbelt–Kitab configuration and 1.1, −5.4 and 4.4 mm with an RMS of 9.7, 13.3 and 24.9 mm for the GA_IDS-2_Datum configuration. The larger variability is reflected in the respective amplitudes. As a comparison, the annual amplitudes of the SLR determined dynamic geocentre are 0.9, 1.0 and 6.8 mm in the X, Y and Z components. The results from this study indicate that there is potential to achieve precise dynamically determined geocentre from DORIS.     

有磁场时电子在航天器光电子鞘层中的漂移运动

采用二级漂移近似理论，研究了在航天器光电子鞘层中与电流收集有关的电子在磁场中的运动轨道和收集电子有关的磁瓶结构，结果表明当磁场越强，航天器表面电势越弱，磁瓶在无穷远处横截面积就越小。在光电子鞘层中，势垒对电流收集影响较大，磁瓶的横截面积在略远于垫垒处有极大值，磁瓶在无穷远处的横截面积并非随着势垒距航天器距离的远近而单调变化。     

Optimal network topology of relative navigation and communication for navigation sharing in fractionated spacecraft cluster

Navigation sharing as a key technology provides orbit and attitude information broadcasting for the whole fractionated spacecraft cluster (FSC). The navigation sharing concept has already been proposed for some years. However, the problem of achieving the optimal navigation sharing by designing the proper network topology is still unsolved, especially in the case that some members of the cluster have absolute navigation devices, some just have relative navigation devices and some only have communication devices. In this paper, a comprehensive model of describing the navigation sharing problem in FSC is proposed. The model of network topology constructing by relative navigation links and communication links is established. By using the graph theory and genetic algorithm as the tool, the conditions for navigation sharing in FSC with different sharing degrees are obtained. Finally, some examples are presented to test the methods, and it has been found that, the absolute positions and attitudes of all the members can still be determined even some members in FSC have no absolute navigation devices.     

Periodic relative orbits of two spacecraft subject to differential gravity and electrostatic forcing

Coulomb forces between charged close-flying satellites can be used for formation control, and constant electric potentials enable static equilibria solutions. In this work, open-loop time-varying potential functions, which produce periodic, two-craft, Coulomb formation motions are demonstrated for the first time. This is done in the rotating Hill-Frame, with linearized gravity, and craft position components assumed in the form of simple harmonic oscillators. Substitution of the oscillatory functions into the dynamics, further constrains these functions, and yields necessary potential histories, to produce the periodic flow. The assumed position functions, however, are not arbitrary, since the dynamical model restricts what oscillatory trajectories are allowed. Specifically, a Hill-Frame integral of motion is derived, and this is used to show certain candidate periodic functions to be inadmissible. The system dynamics are then linearized to expose stability properties of the solutions, and it is established that asymptotic stability is impossible for all orbit families. Finally, the degree of instability in the assumed motions, over free parameter ranges, is determined numerically via the Floquet multipliers of the associated full-cycle state-transition matrices.     

公差原则中相关要求的计算问题

关于公差原则中的相关要求的计算问题 ,本文提出了两种方法 :计算法和图解法。运用这两种方法可以简化此类问题的计算过程 ,准确求得计算结果。     

Evolution of the orbital elements for objects with high area-to-mass ratios in geostationary transfer orbits

A new population of uncatalogued objects in geosynchronous Earth orbits (GEO), with a mean motion of about 1 rev/day and eccentricities up to 0.6, has been identified recently. The first observations of this new type of objects were acquired in the framework of the European Space Agency’s (ESA) search for space debris in GEO and the geostationary transfer orbit (GTO) using the ESA 1-m telescope on Tenerife. Earlier studies have postulated that the perturbations due to the solar radiation pressure can lead to such large eccentricities for GEO objects with a high area-to-mass ratio (A/M). The simulations showed that the eccentricities of GEO objects with large A/M exhibit periodic variations with periods of about one year and amplitudes depending on the value of A/M. The findings of these studies could be confirmed by observations from the ESA 1-m telescope on Tenerife.     

Hybrid optimization for multiple-impulse reconfiguration trajectories of satellite formation flying

A hybrid optimization method is developed for fuel-optimal reconfigurations of a group of satellites flying in formation. The genetic algorithm performs a global search to find two-impulse trajectories, and primer vector analysis finds multiple-impulsive local optimal trajectories with the two-impulse trajectories as initial guesses. Hybrid optimization finds globally optimal trajectories for formation reconfigurations, including formation resizing, reassignment and reorientation maneuvers. Multiple-impulse trajectories reduce the fuel consumption from the two-impulse trajectories by up to 4.4% for those maneuvers. In real missions, satellites can follow two-impulse trajectories to gain the advantage of a smaller number of impulses, with the cost of slightly more propellant. The qualitative characteristics of the optimal trajectories are analyzed from the number of optimal trajectories found by hybrid optimization.     

DPOD2005: An extension of ITRF2005 for Precise Orbit Determination

For Precise Orbit Determination of altimetry missions, we have computed a data set of DORIS station coordinates defined for specific time intervals called DPOD2005. This terrestrial reference set is an extension of ITRF2005. However, it includes all new DORIS stations and is more reliable, as we disregard stations with large velocity formal errors as they could contaminate POD computations in the near future. About 1/4 of the station coordinates need to be defined as they do not appear in the original ITRF2005 realization. These results were verified with available DORIS and GPS results, as the integrity of DPOD2005 is almost as critical as its accuracy. Besides station coordinates and velocities, we also provide additional information such as periods for which DORIS data should be disregarded for specific DORIS stations, and epochs of coordinate and velocity discontinuities (related to either geophysical events, equipment problem or human intervention). The DPOD model was tested for orbit determination for TOPEX/Poseidon (T/P), Jason-1 and Jason-2. Test results show DPOD2005 offers improvement over the original ITRF2005, improvement that rapidly and significantly increases after 2005. Improvement is also significant for the early T/P cycles indicating improved station velocities in the DPOD2005 model and a more complete station set. Following 2005 the radial accuracy and centering of the ITRF2005-original orbits rapidly degrades due to station loss.