Investigation of Conditions for Plane Autorotation of a Spacecraft Entering the Atmosphere

Using the method of averaging, the condition is derived of the regime of plane autorotation for an axisymmetric spacecraft at its initial stage of reentry into the atmosphere, where one can assume the velocity head to be an exponential function of time. The results obtained by this method are compared with the results of numerical calculations. Special attention is given to the regimes of long spacecraft hovering in the vicinity of an unstable equilibrium position. Analytical estimates are made for these regimes.     

Rapid rotations of a satellite with a cavity filled with viscous fluid under the action of moments of gravity and light pressure forces

Rapid rotational motion of a dynamically asymmetric satellite relative to the center of mass is studied. The satellite has a cavity filled with viscous fluid at low Reynolds numbers, and it moves under the action of moments of gravity and light pressure forces. Orbital motions with an arbitrary eccentricity are supposed to be specified. The system, obtained after averaging over the Euler-Poinsot motion and applying the modified averaging method, is analyzed. The numerical analysis in the general case is performed, and the analytical study in the axial rotation vicinity is carried out. The motion in the specific case of a dynamically symmetric satellite is considered.     

Evolution of the Motion of a Viscoelastic Sphere in a Central Newtonian Field

The evolution of translational-rotational motion of a viscoelastic sphere in a central Newtonian field is studied. By the method of separating motions and averaging in the generalized Andoyer–Delaunay variables, equations are derived that describe the evolution of motion. The analysis of the approximate equations obtained is performed. The condition of existence of a steady-state motion is found, and its stability is investigated using the equations in variations.     

Fuel optimum low-thrust elliptic transfer using numerical averaging

Low-thrust electric propulsion is increasingly being used for spacecraft missions primarily due to its high propellant efficiency. As a result, a simple and fast method for low-thrust trajectory optimization is of great value for preliminary mission planning. However, few low-thrust trajectory tools are appropriate for preliminary mission design studies. The method presented in this paper provides quick and accurate solutions for a wide range of transfers by using numerical orbital averaging to improve solution convergence and include orbital perturbations. Thus, preliminary trajectories can be obtained for transfers which involve many revolutions about the primary body. This method considers minimum fuel transfers using first-order averaging to obtain the fuel optimum rates of change of the equinoctial orbital elements in terms of each other and the Lagrange multipliers. Constraints on thrust and power, as well as minimum periapsis, are implemented and the equations are averaged numerically using a Gausian quadrature. The use of numerical averaging allows for more complex orbital perturbations to be added in the future without great difficulty. The effects of zonal gravity harmonics, solar radiation pressure, and thrust limitations due to shadowing are included in this study. The solution to a transfer which minimizes the square of the thrust magnitude is used as a preliminary guess for the minimum fuel problem, thus allowing for faster convergence to a wider range of problems. Results from this model are shown to provide a reduction in propellant mass required over previous minimum fuel solutions.     

自由返回轨道的P平面参数快速设计方法

针对自由返回轨道求解过程中地心轨道类型变化造成的B平面参数方法计算失败问题,提出一种基于P平面参数的自由返回轨道快速设计方法。首先,基于轨道半通径参数的普适性,给出了不同轨道类型的P平面参数定义,建立了以P平面参数为求解目标量的自由返回轨道求解模型。其次,给出了基于P平面参数的自由返回轨道快速设计方法,在构建的瞬时地月惯性系下,以平面双二体自由返回轨道作为初值,实现了高精度力模型下的自由返回轨道快速求解。对8种构型自由返回轨道的设计结果表明,P平面参数具有类似于B平面参数的大收敛域,且有效解决了轨道类型变化对计算的影响,可直接应用于中国后续月球探测任务轨道设计。     

Biaxial Mode of Rotation of a Satellite in the Orbit Plane

A mode of motion of a satellite with respect to its center of mass is studied, which is called the biaxial rotation in the orbit plane. In this mode of rotation, an elongated and nearly dynamically symmetric satellite rotates around the longitudinal axis, which, in turn, rotates around the normal to the plane of an orbit; the angular velocity of rotation around the longitudinal axis is several times larger than the orbital angular velocity, deviations of this axis from the orbit plane are small. Such a rotation is convenient in the case when it is required to secure a sufficiently uniform illumination of the satellite's surface by the Sun at a comparatively small angular velocity of the satellite. The investigation consists of the numerical integration of equations of the satellite's motion, which take into account gravitational and restoring aerodynamic moments, as well as the evolution of the orbit. At high orbits, the mode of the biaxial rotation is conserved for an appreciable length of time, and at low orbits it is destroyed due to the impact of the aerodynamic moment. The orbit altitudes and the method of constructing the initial conditions of motion that guarantee a sufficiently prolonged period of existence of this mode are specified.     

Inter-orbital low-thrust transfers in an arbitrary field of forces

Low-thrust transfers between preset orbits are considered in the presence of perturbations of different origin. A simple method of finding the transfer trajectory is suggested, based on linearization of motion near reference orbits. The required accuracy of calculations is achieved by way of increasing the number of reference orbits. The method can also be used in the case of a large number of revolutions around the attracting center: no averaging of motion is required in this case. The suggested method is applicable as well, when the final orbit is specified partially and when there are constraints on the thrust direction. The optimal solution to the linearized problem is not optimal for the original problem; closeness of solutions to these two problems is estimated using a numerical example. Capabilities of the method are also illustrated by examples.     

太空非合作遥感卫星三维重建点云的平面滤波方法

受太空环境光照条件弱、卫星高速运动、卫星表面纹理匮乏等因素的影响,太空非合作遥感卫星的三维重建点云中往往会存在大量噪声,给太空非合作目标的准确探测带来了非常不利的影响。文章以非合作遥感卫星的形状特征作为先验知识,提出一种三维重建点云的平面滤波方法。针对点云噪声的不同特点,首先利用统计分析滤波方法消除离群离散点噪声;其次,利用改进的区域生长聚类方法,分割出点云模型中的平面结构与离群点簇噪声;然后,分别用RANSAC算法和最小二乘法对平面结构进行滤波,并将平面结构附近的噪声点垂直投影至平面内,去除模型表面噪声。实验结果表明,该优化方法可以有效去除非合作遥感卫星三维重建点云中的大部分噪声,得到卫星平面结构的光滑点云数据。     

基于临界平面法的缺口件疲劳寿命预测方法

利用弹塑性有限元分析得到缺口件的应力、应变历史，分别计算任意材料平面上的描述拉伸和剪切疲劳破坏的两种损伤参量，取最大损伤参量所在的平面为临界平面，并利用最大损伤参量预测拉伸和剪切疲劳寿命，取小值为缺口件的疲劳寿命，进而得到一种预测缺口件疲劳寿命的预测方法。用此方法预测了SAE1045钢缺口件的疲劳寿命，并与实验值进行比较，误差分布在2—3倍因子范围之内。     

Secular evolution of rotary motion of a charged satellite in a decaying orbit

An electrostatically charged Earth satellite whose orbit is decaying due to the Earths oblateness is considered. Secular perturbations of the orbit are taken into account: they are caused by the second zonal harmonic of the geopotential. These perturbations represent deviations of the longitude of the ascending node and perigee argument, the orbit form being invariable and the orbit inclination to the equatorial plane being constant. The attitude rotary motion of the satellite under the action of perturbing moments of the gravitational and Lorentz forces is studied. The magnetic field of the Earth is taken in a quadrupole approximation. The evolution of the satellites rotary motion is investigated on the basis of new differential equations in s-parameters specially constructed for this purpose. Using the method of averaging, basic regularities of the secular evolution of rotary motion of a screened satellite are revealed. It is found that the rotary motion of a charged satellite essentially depends on the quadrupole component of the geomagnetic potential.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 111–125.Original Russian Text Copyright © 2005 by Tikhonov.     

On the breakdown of wave fronts of characteristics in an ideal dissociating gas

Using the method of characteristics, the problem of breaking or non-breaking of waves is studied in a plane cylindrically or spherically symmetric flow of an ideal dissociating gas. It is investigated as to how the effects of dissociation and that of the wave front curvature influence the breaking or non-breaking of waves. In a symmetrical converging gas motion a remarkable difference between the behaviours of cylindrical and spherical waves is discovered.     

Planar oscillations of a vibrating dumbbell-like body in a central field of forces

The problem of planar motions of a dumbbell-like body of variable length in a central field of Newtonian attraction is considered both in the exact formulation and in satellite approximation. In the satellite approximation the true anomaly of the center of mass is used as an independent variable, which has allowed us to represent the equation of planar oscillations of the dumbbell in the form similar to the Beletskii equation. Some exact solutions to the inverse problem are given both in the complete formulation and in satellite approximation. Under an assumption of small orbit eccentricity and amplitude of the dumbbell vibrations the conditions of existence are found for families of almost periodic motions and splitting separatrices. The phenomena of alternation of regular and chaotic motions are established numerically, as well as chaos suppression with increasing frequency of vibrations. Using the method of averaging the stabilization of tangent equilibria is proved to be impossible.     

电磁涡旋波斜平面旋转目标运动参数估计方法

相较于传统平面电磁波,电磁涡旋波具有螺旋分布的波前相位、特殊的环形天线方向图、独特的涡旋方位维信息等特点。近几年来,得益于其特殊的物理特性,电磁涡旋波在目标运动参数估计领域受到了广泛的关注,其目标多普勒效应具有线性多普勒与旋转多普勒两维多普勒信息。现有参数估计方法实现了运动平面与涡旋天线口面平行时的目标旋转参数测量。然而,目标斜平面旋转下,现有方法将不再适用。基于电磁涡旋波所提供的目标旋转多普勒信息,提出一种斜平面旋转目标运动参数估计方法。该方法推导了一般形式下旋转目标的多普勒信号模型,通过分析斜平面下的多普勒信息特征,建立了目标运动参数表征式,给出了斜平面目标旋转参数的计算方法。最后通过仿真分析,验证了模型及参数计算方法的正确性及有效性。     

A study of evolution of spin-up mode of a satellite in the plane of its orbit

We investigate the mode of spinning up a low-orbit satellite in the plane of its orbit. In this mode the satellite rotates around its principal central axis of the minimum moment of inertia which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around this axis several times exceeds the mean orbital motion. Gravitational and restoring aerodynamic moments are taken into account in the satellite’s equations of motion. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape is introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasi-steady-state rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. Such quasi-steady-state rotations are suggested to be considered as unperturbed motions of the satellite in the spin-up mode. Investigation of the integral surface is reduced to numerical solution of a periodic boundary value problem of a certain auxiliary system of differential equations and to calculation of quasi-steady-state rotations by the two-cycle method. A possibility is demonstrated to construct quasi-steady rotations by way of minimization of a special quadratic functional.     

A Celestial Mechanics Model of Oscillations of the Poles of a Deformable Earth

The problem of Chandler motion of the Earth's poles is studied in the context of the model of a viscoelastic body. The Earth-Moon system is considered as a binary planet rotating around their barycenter. Numerical values of the period and amplitudes of oscillations of the poles are obtained by estimating the elastic deformation of the Earth and the variation of its inertia tensor, and they agree well with observational data. An evolution model of the Earth-Moon-Sun system is constructed by taking into account tidal forces of dissipation character. By means of the method of averaging, the qualitative properties of motion on asymptotically large intervals of time (comparable and essentially longer than the period of precession of the Earth's axis) are established and commented on.     

Halo orbits in the vicinity of the L 2 libration point in the Sun-Earth system

Methods are proposed for constructing the orbits of spacecraft remaining for long periods of time in the vicinity of the L ₂ libration point in the Sun-Earth system (so-called halo orbits), and the trajectories of uncontrolled flights from low near-Earth orbits to halo orbits. Halo orbits and flight trajectories are constructed in two stages: A suitable solution to a circular restricted three-body problem is first constructed and then transformed into the solution for a restricted four-body problem in view of the real motions of the Sun, Earth, and Moon. For a halo orbit, its prototype in the first stage is a combination of a periodic Lyapunov solution in the vicinity of the L ₂ point and lying in the plane of large-body motion, with the solution for the linear second-order system describing small deviations of the spacecraft from this plane along the periodic solution. The desired orbit is found as the solution to the three-body problem best approximating the prototype in the mean square. The constructed orbit serves as a similar prototype in the second stage. In both stages, the approximating solution is constructed by continuation along a parameter that is the length of the approximation interval. Flight trajectories are constructed in a similar manner. The prototype orbit in the first stage is a combination of a solution lying in the plane of large-body motion and a solution for a linear second-order system describing small deviations of the spacecraft from this plane. The planar solution begins near the Earth and over time tends toward the Lyapunov solution existing in the vicinity of the L ₂ point. The initial conditions of both prototypes and the approximating solutions correspond to the spacecraft’s departure from a low near-Earth orbit at a given distance, perigee, and inclination.     

一种空间邻近目标红外多传感器立体分辨方法

空间邻近目标在红外像平面的成像因相互交叠而形成簇状像斑,对红外传感器的信号处理提出了分辨的要求。为实现对空间邻近目标的立体跟踪定位,提出基于量子粒子群优化的空间邻近目标红外多传感器立体分辨方法。在对目标像平面成像建模基础上,构建基于最小二乘准则的空间邻近目标立体分辨目标函数,针对目标函数的高维非线性特点,以QP-SO解决目标函数优化问题,估计目标空间位置。仿真结果表明:相比于传统的先单传感器像平面分辨后多传感器视线交叉定位方法,此法具有更优的目标位置估计精度、辐射强度估计精度和目标个数估计正确率。     

空间天文望远镜主动制冷焦面结构设计、分析与热实验

对某天文卫星的可见光望远镜载荷CCD焦面工作温度需求进行了分析计算。为满足CCD焦面 -65℃ 的工作温度需求,设计了主动制冷焦面结构。采用有限元方法分析了工作温度下热电制冷器和导热胶产生的热应力,结果表明热电制冷器最大应力为14Mpa,导热胶最大剪切应力为1.2Mpa,均处于许用安全应力内。研制的焦面组件模拟件顺利通过了真空热试验,验证了焦面组件的制冷性能与安全性。     

基于粘弹性随机有限元的固体推进剂药柱可靠性分析

固体推进剂是一种颗粒填充复合材料，其性能参数具有一定的分散性。为了讨论各类随机因素对药柱结构可靠性的影响，采用局部平均法离散参数随机场，并通过相关结构分解成归一化的独立随机变量，将可靠度指标算法和粘弹性随机有限元法相结合，进行了固体推进剂药柱的结构可靠性分析。算例表明，精度较高，收敛速度较快，适用于工程计算。     

二级入轨空天飞机上升轨迹优化

以最小燃料消耗量为性能指标,考虑了多种约束条件(过载、动压、加热率等 ),采用了组合优化方法对空天飞机上升轨迹进行优化。该组合优化算法包括静态参数与动 态参数优化方法。其中,静态参数优化算法采用了全范围搜索方法,动态参数优化算法包 括动态规划法与共轭梯度法。通过数值仿真计算,得到飞行分离状态数据及相应的最 优 上升轨迹。数值仿真表明,该组合算法对航天器轨迹优化具有良好的适用性及实际工程价 值。