扭转Alfvén波共振的数学描述

提出完备正交函数基(OFSE)展开方法,求解冕环中无耗散扭转Alfvén波.每个基函数对应冕环中每根磁力线的一个固有角频率ωn,当冕环足点驱动频率等于磁力线的固有频率时,Alfvén波将在这根磁力线处发生共振.采用OFSE方法求解了双足点驱动时冕环Alfvén波的时变演化问题,给出了时变解析解的新形式,其中包含共振项,从共振项可以发现,在共振角频率为ω的共振磁力线附近,在时间t为π/ω的整数倍时,出现δ型间断;在t为π/(2ω)的奇数倍时,出现1/x间断.共振磁力线振幅随时间线性增加,增加的斜率正比于Alfvén波速,反比于冕环长度,与驱动频率无关.     

中等相对论性电子环-束引起的束迴旋不稳定性

本文研究了在电子等离子体频率ω_e远大于电子迴旋频率Ω_e的等离子体内,由中等相对论性电子环-束激发的高频(ω≥ω_e)束迴旋不稳定性。结果表明,高能电子束迴旋模在N2cos2θ<1和N2cos2θ>1范围内都是不稳定的,在N2cos2θ=1时是稳定的,这里N为折射指数,θ为传播角。当束迴旋模频率近乎等于冷背景等离子体本征模频率之一(ω≈ω_e)时增长率最大。文中介绍和讨论了色散方程的数值计算结果。      

月球卫星轨道设计优化

利用带谐项J2和J3对月球卫星轨道进行了优化设计．首先分析了月球卫星轨道摄动因素对轨道的影响，其次推导了对应于J2和J3项的冻结轨道计算公式，并通过对仅包含月球引力场模型的运动微分方程，直接积分计算轨道的变化进行了验证．最后，通过合理选择初始轨道的偏心率e0和近月点幅角ω0，对月球卫星极轨道进行了优化设计，给出了设计公式并进行了仿真．结果表明，这种优化设计方法是很有效的．     

太阳质量损失对行星轨道的影响

本文利用Ｇｙｌｄｅｎ－Ｍｅｓｈｃｈｅｒｓｋｉｉ方程和Ｅｄｄｉｎｇｔｏｎ－Ｊｅａｎｓ定律，讨论太阳质量损失对行星轨道的影响，结果表明由于太阳质量损失会产生轨道半长径α的一阶周期项和二阶混合项；近日点角距ω的一阶周期项、二阶长期项和混合项，行星轨道半长径的长期变化会影响太阳系的稳定性。     

不定方程x~4+y~4+z~4=ω~2的解

本文论证了不定方程x~4+y~4+z~4=ω~2存在正整数解,并给出了解的表达式,从而为讨论不定方程x~4+y~4+z~4=ω~4是否存在正整数解奠下了基石。     

卫星空间外热流轨道参数ψo,Ωo和ωo计算

文章给出了卫星热分析空间外热流计算中所需要的轨道参数太阳黄经，升交点赤经和近地点幅角的初值ψｏ，Ωｏ和ωｏ的计算公式。其精确度满足卫星热分析要求。     

关于HEO空间飞行体的轨道寿命问题

低轨地球卫星的轨道寿命主要取决于大气的耗散作用,其轨道在不断变小(即高度降低)变圆的状态下进入地球稠密大气层中陨落.但HEO(Highly Eccentric Orbit)类型的空间飞行体的运行轨道是一个近地点高度很低,远地点高度却很高的大偏心率椭圆轨道,其轨道寿命主要由第三体(日、月)引力摄动所决定,而且还与其轨道的初始状态有密切关系,特别是慢变量Ω(轨道升交点经度)和ω(轨道近地点幅角),决定了偏心率e的长周期变化状态,从而制约了HEO类型空间飞行体的轨道寿命.本文将根据地球卫星轨道变化规律进行理论分析,阐明这一力学机制,并给出相应的数值验证.      

电离层中SEE现象的静电粒子模拟

利用网格粒子云（PIC）模型。在一定条件下，对电离层加热实验中静电波的激发和参量不稳定性的产生，作一维静电粒子模拟，模拟结果表明，SEE的特征与加热泵波频率ω0和电子回旋频率nωce之间的比值有关。入射泵波的电场与地磁场之间的夹角也是影响SEE的一个因素。     

卫星空间外热流轨道参数ψ_0,Ω_0和ω_0计算

文章给出了卫星热分析空间外热流计算中所需要的轨道参数太阳黄经、升交点赤经和近地点幅角的初值φ_0、Ω_0、ω_0 的计算公式。其精确度满足卫星热分析要求。     

金属混合断口的宏观定量分析

本文在分析拉伸试样发生缩颈时的屈服方式的基础上,给出由拉伸数据估算J积分值的近似公式:J=ak(a/b,m)ηI;并给出计算拉伸断口的纤维区尺寸、剪切唇尺寸的粗略的近似公式: 2a/d≈(n 3.87/n~2 7.74n 14.17)ψ 0.05和ψ≈((n′)~2 2n′ 0.3)/(n′ 1)(S/(d/2 0.77)     

Satellite orbits in Levi-Civita space

In this paper we consider satellite orbits in central force field with quadratic drag using two formalisms. The first using polar coordinates in which the satellite angular momentum plays a dominant role. The second is in Levi-Civita coordinates in which the energy plays a central role. We then merge these two formalisms by introducing polar coordinates in Levi-Civita space and derive a new equation for satellite orbits which unifies these two paradigms. In this equation energy and angular momentum appear on equal footing and thus characterize the orbit by its two invariants. Using this formalism we show that equatorial orbits around oblate spheroids can be expressed analytically in terms of Elliptic functions. In the second part of the paper we derive in Levi-Civita coordinates a linearized equation for the relative motion of two spacecrafts whose trajectories are in the same plane. We carry out also a numerical verification of these equations.     

小天体环的轨道动力学

随着天文观测的深入,发现不仅土星、木星等气态巨行星环绕有光环,某些小天体也环绕有光环。针对目前发现环的半人马型小天体女凯龙星（10199 Chariklo）,研究其引力场中粒子（视为质点）的轨道动力学,分析赤道椭率和小天体自转对环中粒子轨道运动的影响,通过庞加莱截面中的KAM环迭代,得到第一类周期轨道和1∶3共振周期轨道,并通过对比和分析得到小天体光环位置与小天体自转平运动共振的关系。研究结果表明:女凯龙星内环中的粒子最可能处在满足径向振荡幅值范围的第一类周期轨道及其附近的准周期轨道上,但不能排除处在1∶3共振周期轨道及其附近的准周期轨道上;外环中的粒子不可能处在1∶3共振周期轨道上,只可能处在第一类周期轨道及其附近的准周期轨道上。      

Dynamical evolution of high area-to-mass ratio objects in Molniya orbits

For special demands, some notable orbit types have been developed by human, including the Molniya orbits, which have a relatively high eccentricity up to about 0.7, and a period of 12 h. Considering that space debris with high area-to-mass ratio (A/M) has been discovered, such objects may also exist in Molniya orbits due to spacecraft and upper stages fragmentation events. However, there are not sufficient studies of the complex dynamical phenomena of such orbits. These studies can enrich the knowledge about the long-term evolution of these orbits, be helpful to propose uncatalogued objects observation and identification, and also set the protected region as well as active debris removal. In this paper, the characteristics of 2:1 resonance of Molniya satellite orbits are studied. A large set of numerical simulations, including all the relevant perturbations, is carried out to further investigate the main characteristics, and special attention is payed to the dynamical evolution of objects with high A/M, particularly affected by the direct solar radiation pressure. The long-term dynamical evolution of orbital elements, as well as the dependency of lifetime on the A/M value, is discussed.     

火卫一周期准卫星轨道及入轨分析

围绕火卫一的准卫星轨道（QSOs）因其具有良好的稳定性,是火卫一探测任务最为实用的轨道。在平面圆型限制性三体问题模型下,利用庞加莱截面和KAM环迭代方法探究了准卫星轨道的周期轨道族,并给出不同能量准卫星周期轨道的初始条件。针对火卫一周期准卫星轨道入轨,提出一种转移轨道设计方法:对准卫星周期轨道调整速度后进行反向积分,直至离开火卫一邻近区域,从而得到由火星环绕轨道向火卫一周期准卫星轨道的转移轨道,并调整转移轨道参数对燃料与时间消耗进行优化。研究结果表明,当周期准卫星轨道能量处于特定区间时,存在特定速度脉冲区间,可利用火卫一引力实现较少燃料消耗的轨道转移;在该速度脉冲区间中,通过选取较小的速度脉冲,可缩短转移时间。      

真空中连续发射电子束形成的电子鞘层的空间结构

用双流理论模型研究真空中电子束的发射实验。向真空中发射电子束过程中,发射体本身被充正电,束缚束电子向外传播,大量的束电子在发射体表面附近形成电子鞘层;只有极少量的束电子可以逃离发射体而向外传播出去。在电子鞘层内,发射出的束电子和返回发射体表面的束电子形成速度和密度在空间为分布不均匀的双流。本文用双流理论模型解析计算出了电子鞘层的空间尺度、电子鞘层内的电场分布以及电子密度分布。      

Towards development of a consistent orbit series for TOPEX,Jason-1, and Jason-2

The TOPEX/Poseidon, Jason-1 and Jason-2 set of altimeter data now provide a time series of synoptic observations of the ocean that span nearly 17 years from the launch of TOPEX in 1992. The analysis of the altimeter data including the use of altimetry to monitor the global change in mean sea level requires a stable, accurate, and consistent orbit reference over the entire time span. In this paper, we describe the recomputation of a time series of orbits that rely on a consistent set of reference frames and geophysical models. The recomputed orbits adhere to the IERS 2003 standards for ocean and earth tides, use updates to the ITRF2005 reference frame for both the SLR and DORIS stations, apply GRACE-derived models for modeling of the static and time-variable gravity, implement the University College London (UCL) radiation pressure model for Jason-1, use improved troposphere modeling for the DORIS data, and apply the GOT4.7 ocean tide model for both dynamical ocean tide modeling and for ocean loading. The new TOPEX orbits have a mean SLR fit of 1.79 cm compared to 2.21 cm for the MGDR-B orbits. These new TOPEX orbits agree radially with independent SLR/crossover orbits at 0.70 cm RMS, and the orbit accuracy is estimated at 1.5–2.0 cm RMS over the entire TOPEX time series. The recomputed Jason-1 orbits agree radially with the Jason-1 GDR-C orbits at 1.08 cm RMS. The GSFC SLR/DORIS dynamic and reduced-dynamic orbits for Jason-2 agree radially with independent orbits from the CNES and JPL at 0.70–1.06 cm RMS. Applying these new orbits, and using the latest altimeter corrections for TOPEX, Jason-1, and Jason-2 from September 1992 to May 2009, we find a global rate in mean sea level of 3.0 ± 0.4 mm/yr.     

Propagation errors analysis of TLE data

Orbit position uncertainty is an important factor for collision avoidance issues. For a single object with high frequency historical data, we can attain its position uncertainty easily. But sometimes data is not enough for errors analysis, orbits need to be classified. In this paper error analysis is made from two-line element sets data (TLEs). The Simplified General Perturbations-4 (SGP4) propagator was used. Statistical errors of debris and R/B are given for lower-altitude orbits which are classified by perigee altitude and eccentricity. The errors results and analysis for SSO (the Sun synchronous orbit) typical orbits are obtained. At last atmospheric drag as a main cause of downrange errors in lower-altitude orbit is analyzed. BSTAR in TLEs is modified to improve prediction precision.     

Face-dependent impact probabilities, velocities and angles upon LDEF by space debris and natural meteoroids

For specified geocentric orbits the impact probabilities, velocities and angles upon the different faces of the Long Duration Exposure Facility (LDEF) are calculated, and it is found that quite different distributions of micro-cratering are to be expected. In particular the flux to the East (leading) face should exceed that to the West (trailing) face by a very large ratio. The North and South faces receive exposures slightly in excess of the East face for lower-velocity impacts from low-inclination orbits, but much lower exposures than the East face for high-velocity impacts from high-inclination orbits. The Space face (pointing directly away from the Earth) and the Earth face (pointing directly towards the Earth) will have been subject to very few impacts from geocentric orbits. Therefore, whilst three sides (the East, North and South) will have been hit many times by artificial space debris, the other three (the West, Space and Earth) will have been impacted almost solely by natural meteoroids from heliocentric orbits, and may be used to determine the flux of such particles in the vicinity of the Earth. The ratios of impacts upon the East, West and Space faces will be useful indicators of the velocity/orbit distribution of meteoroids.     

椭圆轨道编队的构形变化控制方法

推导了椭圆轨道编队的一些典型构形模态,指出椭圆轨道卫星编队的模态不同于圆轨道的构形模态,是极为丰富的。基于T-H方程的解析解,推导了副星在沿航向常值推力作用下的椭圆轨道编队的构形变化控制方法。推导的构形变化控制方法,通过合理的选择控制量的作用时刻,可达到大量节约燃料的目的。最后,给出仿真算例。