卫星编队飞行中C-W方程与轨道根数法的比较

目前卫星编队飞行动力学与控制的研究得到了广泛的重视,这些研究的理论主要是基于描述卫星相对运动的Clohessy-Wiltshire(C-W)方程。但根据特例及定性分析,表明C-W方程在初始条件的选取、解的周期性等方面与实际情况不符,从星的能量也不守恒。以卫星轨道根数为基础,提出了卫星编队飞行中的相对轨道根数法,克服了C-W方程的局限性,物理概念清楚,应用范围广,解的周期性成为自然结论。在主星为小偏心率的情况下,得到了简化的相对运动方程。最后对两种方法进行了比较,指出了C-W方程的局限性及其原因。     

卫星编队飞行轨道和姿态控制研究

卫星编队飞行是一种卫星应用的新概念,通过一系列造价更便宜的小卫星的分布式合作,代替大卫星实现复杂功能．在编队飞行一些应用中,要求受控卫星对目标卫星保持要求的相对位置和姿态以观察目标卫星的特定面,特别的,目标卫星可能是失效的．研究在近地轨道如何控制追踪星在失效的目标卫星附近飞行以追踪目标卫星特定面 的问题,给出了相对姿态和一阶近似的相对轨道动力学方程．基于线性反馈和Liapunov稳定性理论设计了控制策略．进一步的,考虑目标卫星转动惯量的不确定性,通过自适应控制的方法,获得正确的转动惯量比率．数值仿真算例验证了该控制方法的有效性．     

地球引力场对卫星有摄运动的一种计算方法

本文应用Delaunay变量,从理论力学的哈密顿方程出发,通过正则变换求解了地球引力摄动对卫星运动轨道的影响,导出卫星位置和速度随时间的变化关系.     

纯引力轨道验证质量辐射计效应分析

纯引力轨道飞行器在精密导航、重力场测量以及基础科学研究等方面具有重要意义,辐射计效应是纯引力轨道验证质量的重要干扰力之一．针对内编队重力场测量系统,利用解析和数值计算相结合的方法,分析了内卫星辐射计效应与内编队系统参数的关系,并给出了适宜于工程计算的内卫星辐射计效应近似函数及其修正因子．分析可知,内卫星辐射计效应与腔体平均压力成正比,与腔体平均温度成反比;随腔体温差的增加而增加,随外卫星腔体半径的增加存在极小值,并且取极小值时外卫星腔体半径和内卫星半径比为常数1.189 4,这一常数是由内外卫星的球形腔体构型决定的,与腔体内温度和压力无关．当内外卫星半径比大于10时,可认为外卫星腔体充分大,此时内卫星辐射计效应与内卫星半径的平方近似成正比,随外卫星腔体半径的变化可忽略．     

非正则形式的变换方法及其应用

在文献[1]中讨论各种变换方法时,曾简要地提出了一种非正则形式变换方法的轮廓,本文将进一步详细地介绍该方法的原理、过程和两种形式、(隐形式和显形式).最后,作为一个例子,给出小天体在主星扁率摄动下的运动解。     

基于不变流形的登月轨道设计

研究了基于三体问题的不变流形设计低成本登月轨道的问题．考虑了黄道面和白道面之间夹角不为零的三维情况,将太阳-地球-月亮-卫星组成的四体问题分解成由太阳-地球-卫星和地球-月亮-卫星组成的非共面的两个限制三体问题．给出了这两个三体系统Halo轨道不变流形与两轨道面相交处进行小的变轨来设计低成本探月轨道的一般方法．比较结果表明用该方法设计的轨道比传统的Hohmann变轨节省约20%的燃料．从轨道能量的角度分析了用流形设计轨道比Hohmann变轨节省燃料的原因,并给出了理论表达式．该方法对于深空探测轨道设计的能量分析具有普遍的适用性,可为设计提供一个选择参数的标准．     

考虑环影响的平面圆型限制性三体问题的可能运动区域

本文讨论了一个主星体带环的平面圆型限制性三体问题的可能运动区域,给出了第三体的运动方程,并得到下面一些结论:(1)秤动点的位置依赖于系统的参数μ;环的内、外半径a,b;两主星体之间距离l;以及环的质量与带环主星体与环的总质量之比θ.当a,b,l,θ一定时,秤动点的个数随μ变化,最多有五个,最少有三个.此外,三角秤动点与两个主星体的构形是等腰三角形.(2)当a,b,l,θ一定时,给出了系统参数μ的一个变化范围,当μ在这个范围内时,第三体可能运动区域的结构与通常意义下的平面圆型限制性三体问题的相似.     

行星悬浮轨道附近的编队

研究了不同类型的地球和火星悬浮轨道附近的相对运动．首先,推导了悬浮轨道附近的相对运动方程并将相对运动方程在悬浮轨道附近线性化．利用两种半自然编队控制率进行编队控制,其中一种为被动控制,对工程应用有很大的价值．在两种控制率下,讨论了每种悬浮轨道的稳定区域．由于两种控制率都不能满足特殊的火星悬浮轨道任务要求,于是,根据该任务的要求设计了一种特殊的半自然控制率．该控制率既能满足编队任务的要求也能使相对运动稳定．     

对地观测卫星过顶预报与定轨模型的建立

针对某些对地观测卫星,其轨道参数不公开,只能通过对卫星的运行规律建立数学模型,推导出卫星的过顶时间,从而使对地目标有效规避卫星的对地观测.首先从卫星运行的基本规律出发,根据稀疏数据进行定轨建立了卫星定轨的数学模型,利用牛顿迭代法递推出轨道根数,同时利用摄动补偿优化了模型,再通过八阶龙格库塔法,进行轨道递推,得到了卫星过顶时间与轨道信息的对应关系.     

轨道运动方程数值解的一种加速算法

针对卫星轨道受大气阻力摄动的运动方程,提出了一种数值加速算法,该算法实现简单、计算量小、精度高,适合于各类卫星轨道的方程的求解.     

On manifolds of initial conditions leading to intersection of orbits of satellites with planet under weak gravitational perturbations

We consider the problem of initial conditions that lead to the intersection of a satellite orbit with planetocentric sphere of a radius R. The problem is considered in frame of the satellite version of the double-averaged restricted three body problem with taking into account gravitational perturbations caused by the polar oblateness of the planet. For some integrable cases we provide the boundaries of the manifolds of the initial orbital elements leading (or not leading) to the intersection of the satellite orbit with the planet surface.     

Linear problems of the stability of a type of rotation of a satellite about the centre of mass

The stability in the first approximation of the rotation of a satellite about a centre of mass is investigated. In the unperturbed motion the satellite performs, in absolute space, three rotations around the normal to the orbital plane in a time equal to two periods of rotation of its centre of mass in the orbit (Mercury-type rotation). Three cases of such rotations are considered: the rotations of a dynamically symmetrical satellite and a satellite, the central ellipsoid of inertia of which is close to a sphere, in an elliptic orbit of arbitrary eccentricity, and the rotation of a satellite with three different principal central moments of inertia in a circular orbit.     

Non-linear oscillations of a satellite at 1:1:1 resonance

The motion of a satellite about its centre of mass in a central Newtonian gravitational field is investigated. The satellite is considered to be a dynamically symmetrical rigid body. It is assumed that the ratio of the polar and equatorial principal central moments of inertia of the satellite is 4/3, or close to this. The orbit of the centre of mass is elliptic, and the orbit eccentricity is assumed to be small. In the limit case, when the orbit of the centre of mass is circular, a steady motion exists (corresponding to relative equilibrium of the satellite in the orbital system of coordinates) in which the axis of dynamic symmetry is directed along the velocity vector of the centre of mass of the satellite; here, the frequencies of the small linear oscillations of the axis of symmetry are equal or close to one another. But in an elliptic orbit of small eccentricity, multiple 1:1:1 resonance occurs in this case, as the oscillation frequencies mentioned are equal or close to the frequency of motion of the centre of mass of the satellite in orbit. The non-linear problem of the existence, bifurcations and stability of periodic motions of the satellite with a period equal to the rotation period of its centre of mass in orbit is investigated.     

The oscillations of a satellite about a direction fixed in absolute space

The stability of the plane oscillations of a satellite about the centre of mass in a central Newtonian gravitational field is investigated. The orbit of the centre of mass is circular and the principal central moments of inertia of the satellite are different. In unperturbed motion, one of the axes of inertia is perpendicular to the plane of the orbit, while the satellite performs periodic oscillations about a direction fixed in absolute space. The problem of the stability of these oscillations with respect to plane and spatial perturbations is investigated.     

Rotations of a near-symmetrical satellite in an elliptical orbit with Mercury-type resonance

The motion of a satellite, i.e., a rigid body, about to the centre of mass under the action of the gravitational moments of a central Newtonian gravitational field in an elliptical orbit of arbitrary eccentricity is investigated. It is assumed that the satellite is almost dynamically symmetrical. Plane periodic motions for which the ratio of the average value of the absolute angular velocity of the satellite to the average motion of its centre of mass is equal to 3/2 (Mercury-type resonance) are examined. An analytic solution of the non-linear problem of the existence of such motions and their stability to plane perturbations is given. In the special case in which the central ellipsoid of inertia of the satellite is almost spherical, the stability to spatial perturbations is also examined, but only in a linear approximation. ©2008.     

On the stability of a satellite cylindrical precession in an elliptic orbit : PMM vol. 40, n 6, 1976, pp. 1040–1047

The stability of motion of a dynamically symmetric satellite with respect to its center of mass in a central Newtonian gravitational field is investigated. The satellite is a solid body whose center of mass moves on an elliptic orbit. The particular case in which the satellite axis of symmetry is normal to the orbit plane (the so-called cylindrical precession [1, 2]) and its absolute angular velocity projection on the axis of symmetry is zero, is examined. Analytical and numerical methods are used. Regions of Liapunov instability and of stability in the first approximation are. obtained in the parameter space of the problem (the inertial parameter and the orbit eccentricity). Detailed nonlinear analysis is carried out in the latter, and the formal stability of the satellite cylindrical precession is proved. The question of stability for the majority of intial conditions is also considered [4].     

Bifurcations of the relative equilibria of a gyrostat satellite for a special case of the alignment of its gyrostatic moment

The bifurcations of the equilibria of a gyrostat satellite with a centre of mass moving uniformly in a circular Kepler orbit around an attracting centre are investigated. It is assumed that the axis of rotation of a statically and dynamically balanced flywheel rotating at a constant relative angular velocity is fixed in the principal central plane of inertia of the gyrostat containing the axis of its mean moment of inertia and that it is not collinear with any principal central axis of inertia of the system. The problem is solved in a direct formulation, that is, the whole set of equilibria with respect to the orbital system of coordinates of the gyrostat satellite is determined using the given moments of inertia, the value of the gyroscopic moment and the direction cosines of the axis of rotation of the flywheel and the changes in this set are investigated as a function of the bifurcation parameter, that is, the magnitude of the gyrostatic moment of the system. A parametric analysis of the relative equilibria of the three possible classes of equilibria for a system in a circular orbit in a central Newtonian force field is carried out using computer algebra facilities.     

A Study of the Motions of an Autonomous Hamiltonian System at a 1:1 Resonance

We examine the motions of an autonomous Hamiltonian system with two degrees of freedom in a neighborhood of an equilibrium point at a 1:1 resonance. It is assumed that the matrix of linearized equations of perturbed motion is reduced to diagonal form and the equilibrium is linearly stable. As an illustration, we consider the problem of the motion of a dynamically symmetric rigid body (satellite) relative to its center of mass in a central Newtonian gravitational field on a circular orbit in a neighborhood of cylindrical precession. The abovementioned resonance case takes place for parameter values corresponding to the spherical symmetry of the body, for which the angular velocity of proper rotation has the same value and direction as the angular velocity of orbital motion of the radius vector of the center of mass. For parameter values close to the resonance point, the problem of the existence, bifurcations and orbital stability of periodic rigid body motions arising from a corresponding relative equilibrium of the reduced system is solved and issues concerning the existence of conditionally periodic motions are discussed.     

A method for analytically representing area-preserving mappings

An area-preserving mapping is considered. It is assumed that the mapping has a fixed point and is analytic in a small neighbourhood near it. A constructive algorithm for obtaining a representation of the mapping in the form of a composite of two area-preserving mappings, one of which is a nearly identity mapping, while the other corresponds to the real normal form of a linearized mapping, is described. The algorithm is used in the problem of the stability of the translational motion of a rigid body in a uniform gravitational field when it undergoes collisions with a fixed horizontal plane and in the problem of the stability of one type of resonant in-plane rotations of a satellite, i.e., a rigid body, in an elliptic orbit.     

Transient times,resonances and drifts of attractors in dissipative rotational dynamics

In a dissipative system the time to reach an attractor is often influenced by the peculiarities of the model and in particular by the strength of the dissipation. As a dissipative model we consider the spin–orbit problem providing the dynamics of a triaxial satellite orbiting around a central planet and affected by tidal torques. The model is ruled by the oblateness parameter of the satellite, the orbital eccentricity, the dissipative parameter and the drift term. We devise a method which provides a reliable indication on the transient time which is needed to reach an attractor in the spin–orbit model; the method is based on an analytical result, precisely a suitable normal form construction. This method provides also information about the frequency of motion. A variant of such normal form used to parameterize invariant attractors provides a specific formula for the drift parameter, which in turn yields a constraint – which might be of interest in astronomical problems – between the oblateness of the satellite and its orbital eccentricity.