Generalized restricted circular three-body problem as a model for dynamics of binary asteroids

Exploration of the Solar System has recently revealed the existence of a large number of asteroids with satellites, which has stimulated interest in studying the dynamics of such systems. This paper is dedicated to the analysis of the relative motion of a binary asteroid. The conditions of existence of such a system (i.e., when its components do not run away) are derived in the Introduction. Then it is assumed that the satellite has no significant effect on the motion of the main asteroid, the latter being modeled as a dumbbell-like precessing solid body. The equations of motion of this system are a two-parameter generalization of the corresponding equations of the restricted circular three-body problem. It is demonstrated that in the system under consideration there exist steady-state motions in which the small asteroid is equidistant from attracting centers at the ends of the dumbbell (an analog to triangle libration points). The conditions of existence of such motions are derived, and the positions with respect to the dumbbell are analyzed in detail. Examination of the stability of the triangle libration points is reduced to investigation of a characteristic equation of the sixth degree. The stability conditions are derived in the case when the main asteroid executes near-planar motion.     

Existence of nonimpact motions along a wire rope fixed to an extended spacecraft

The possibility of nonimpact tension of a cable after its weakening when a small load moves along the cable whose ends are fixed on a massive dumbbell-like spacecraft which is moving in a steady-state manner along a circular orbit is considered. The conditions of existence and classification of the trajectories of nonimpact motion, including periodic ones, are presented.     

On the planar inertial motion of a system of three coupled bodies

Numerous papers are devoted to studying the motion of a system (coupling) of two bodies in the Earth’s satellite orbit ([1–4] and others). The problem on the planar inertial motion of three bodies, coupled by a non-extensible weightless string having the form of an unfastened chain, is considered in the paper. Such a configuration can be represented, for example, by a system of two coupled spacecraft rotating around their common center of mass (in order to simulate the gravity force) in long-term space missions, when the third body (the lift) is located on a connecting cable. The bodies are considered to be the material points (particles).     

Stability of triangle libration points in generalized restricted circular three-body problem

Equilibrium positions of a small-mass body are considered with respect to a precessing dumbbell. The dumbbell represents two rigidly fixed spherical gravitating bodies. Such a system can be considered as a model of a binary asteroid. Stability of relative equilibrium positions with equal distances from the small mass to the attracting centers is studied. By analogy with the classical restricted three-body problem, these positions are referred to as triangle libration points. It is shown that the character of stability of these libration points is determined by three constant parameters: nutation angle and angular velocity of precession, as well as the ratio of masses at the ends of the dumbbell. Stability conditions are derived in the linear approximation, and the regions of stability and instability in the space of problem parameters are constructed. The paper is a continuation of [1].     

Translational–Rotational Motion of a Viscoelastic Sphere in Gravitational Field of an Attracting Center and a Satellite

We study the translational–rotational motion of a planet modeled by a viscoelastic sphere in the gravitational fields of an immovable attracting center and a satellite modeled as material points. The satellite and the planet move with respect to their common center of mass that, in turn, moves with respect to the attracting center. The exact system of equations of motion of the considered mechanical system is deduced from the D'Alembert–Lagrange variational principle. The method of separation of motions is applied to the obtained system of equations and an approximate system of ordinary differential equations is deduced which describes the translational–rotational motion of the planet and its satellite, taking into account the perturbations caused by elasticity and dissipation. An analysis of the deformed state of the viscoelastic planet under the action of gravitational forces and forces of inertia is carried out. It is demonstrated that in the steady-state motion, when energy dissipation vanishes, the planet's center of mass and the satellite move along circular orbits with respect to the attracting center, being located on a single line with it. The viscoelastic planet in its steady-state motion is immovable in the orbital frame of reference. It is demonstrated that this steady-state motion is unstable.     

On a lunar space elevator

We consider a space elevator system for lunar surface access that consists of a space station in circumlunar orbit, a cable reaching down to some meters above the surface and a magnetically levitated vehicle driven by a linear motor. It accelerates the load to be lifted to the speed of the cable end. Loads to be delivered are either put on the vehicle and slowed down by it or they are slowed down by a sand braking technique in a mare terrain. It is technically possible to operate this transport system nearly without fuel supply from Earth. We calculate various steel cable dimensions for a static stress maximum of $\text{1}\text{5}\text{th}$ of the tensile strength. The process of takeover is considered in detail. Five ways of eliminating the adverse large cable elongation due to the load are described. The touchdown process and behaviour of the cable after disconnection are analysed. The positive difference between the speed of the load at takeover and cable end can excite a large inplane swing motion. We propose to damp it by a dissipative pulley that hangs in a loop of wire leading to the ends of two beams mounted on the space station tangentially to the orbit, the pulley's core being connected with the load. Roll librations are damped by energy losses in the elastic beams; damping can be reinforced by viscous beam elements and/or controlled out-of-plane motions of the beams. We argue in favour of the possibility of fast deployment. The problems of vehicle vibrations and agglutination at sand braking blades are underlined and their combined experimental investigation is suggested.     

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.     

柔索驱动式航天员虚拟微重力训练系统控制与实验

针对现有的航天员地面微重力训练设备存在成本高、单次训练时间短、模拟精度低等问题,提出了一种柔索驱动的航天员虚拟微重力训练系统。通过采样航天员对作业对象的操作力,控制柔索驱动虚拟物体(末端执行器)运动,使虚拟物体符合在微重力环境中的运动规律。建立了柔索驱动训练系统的动力学模型,分析了系统的特性。针对传统力伺服系统多余力对控制力精度影响较大且难以克服的问题,提出了一种使用弹簧产生柔索张力的并联柔索全位置型控制方法,并引入力/速局部反馈的控制策略。实验结果表明,系统克服多余力效果明显,可以获得较高的驱动力控制精度;虚拟质量在操作力作用下的运动符合在微重力环境中的运动规律,且有较高的模拟精度;系统稳定性良好,可以实现微重力环境中移动不同质量物体的虚拟作业训练。     

柔性绳网动力学建模与天地差异性分析

采用有限元模型研究了柔性绳网系统的动力学特性。针对空间绳网直接弹射展开方式,首先将绳网离散为若干单元,各单元处理为非线性“半阻尼弹簧”模型,然后分别计算各单元所受气动力和重力,最终建立绳网系统多柔体动力学模型。基于所建立的动力学模型分别对柔性绳网在地面和太空展开的动力学过程进行了仿真分析,研究了绳网在展开面积、空间位形和飞行距离等方面的天地差异性及其动力学机理,为未来空间绳网系统的分析设计提供理论参考。     

Features of rotational motion of a spacecraft descending in the Martian atmosphere

Angular motion at atmospheric entry is studied in the paper for a spacecraft with a bi-harmonic moment characteristic. Special attention is given to the case when the spacecraft possesses two stable balanced positions, and, hence, it can oscillate in dense atmospheric layers in the ranges of small or large angles of attack. The averaged equations of spacecraft motion are derived, which allow one to increase the speed of calculations by several orders of magnitude. A real example is presented, which concerns a spacecraft specially designed for descending in the Martian atmosphere.     

Geostationary station keeping control of a space elevator during initial cable deployment

This paper presents a basic concept to derive an orbital control strategy to achieve the full deployment and the geostationary station keeping of a space elevator during its initial cable deployment. The space elevator model is composed of a main spacecraft, a sinker mass and a massive cable connecting them. The cable elasticity, flexibility and taper of the cross-sectional area are omitted for simplification. A reference trajectory is designed so that the space elevator and its center of mass ascend vertically along the geostationary position with keeping the geostationary orbital rate. From the reference trajectory analyses, an orbital control that leads the space elevator orbit to the reference one is derived. However it is found that the reference trajectory is unstable throughout the deployment and a linear feedback control is introduced for stabilization. It is also clarified that the libration destabilizes the orbital control because the orbital acceleration caused by the libration always acts in the opposite direction to the orbital control. Therefore, a libration control is also introduced to stabilize the coupled orbital and librational motions. Numerical simulation result clearly shows that these controls facilitate the full deployment and the geostationary station keeping of the space elevator within the feasible thrust force and amount of propellant.     

The effect of the configuration and the interior design of a virtual weightless space station on human spatial orientation

In a virtual weightless environment, subjects’ orientation skills were studied to examine what kind of cognitive errors people make when they moved through the interior space of virtual space stations and what kind of visual information effectively decreases those errors. Subjects wearing a head-mounted display moved from one end to the other end in space station-like routes constructed of rectangular and cubical modules, and did Pointing and Modeling tasks. In Experiment 1, configurations of the routes were changed with such variables as the number of bends, the number of embedding planes, and the number of planes with respect to the body posture. The results indicated that spatial orientation ability was relevant to the variables and that orientational errors were explained by two causes. One of these was that the place, the direction, and the sequence of turns were incorrect. The other was that subjects did not recognize the rotation of the frame of reference, especially when they turned in pitch direction rather than in yaw. In Experiment 2, the effect of the interior design was examined by testing three design settings. Wall colors that showed the allocentric frame of reference and the different interior design of vertical and horizontal modules were effective; however, there was a limit to the effectiveness in complicated configurations.     

On plane oscillations of a pendulum with variable length suspended on the surface of a planet’s satellite

The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We discuss how the change in length of a pendulum can be used to compensate its oscillations. We wrote equations of motion, indicated a rule for the change in length of a pendulum, at which it has equilibrium positions relative to the coordinate system rotating together with the Moon and Earth. We study the necessary conditions for the stability of these motions. Chaotic dynamics of the pendulum is studied numerically and analytically.     

The Mode of Gravitational Orientation for the International Space Station

The results of the determination of the uncontrolled attitude motion of the International Space Station during its unmanned flight in 1999 are presented. The data of onboard measurements of three components of the angular velocity are used for this determination. These data covering an interval of slightly less than one orbit were jointly processed by the least squares method, by integrating the equations of motion of the station relative to its center of mass. As a result of this processing, the initial conditions of the motion and the parameters of the mathematical model used were estimated. The actual motion of the station has been determined for 20 such intervals during April–November. Throughout these intervals, the station rotated about the axis of the minimum moment of inertia, the latter executing small oscillations relative to the local vertical. Such a mode, known as the mode of gravitational orientation of a rotating satellite or the mode of generalized gravitational orientation, was planned before the flight. The measurements were made to verify it. The quasistatic component of the microaccelerations aboard the station is estimated for this mode.     

面向卫星追踪平台的容错纠错策略与算法研究

针对2RPS+2TPS型卫星追踪平台可能出现的传感器故障提出了一种容错纠错策略。该策略通过在卫星追踪平台的固定平台和动平台中心附加一柔索,柔索一端连接弹簧和冗余传感器,实现了对卫星追踪平台四条驱动腿传感器故障的容错纠错功能。如果驱动腿中的某一个传感器发生故障,则可根据空间闭链机构约束,由其它正常工作驱动腿的传感器和冗余传感器的测量值计算出故障传感器的应测值。推导出了位移和速度传感器故障的容错纠错重构算法。通过模拟渐变型和突变型的传感器故障,对提出的容错纠错方案进行了仿真研究,仿真结果表明提出的容错纠错策略能有效地保障卫星追踪平台系统运行的可靠性和安全性。
     

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.     

测量设备站点安装对中误差修正方法

靶场大型机动站精密测量设备在站点安装时,通常不能做到设备的回转中心与站点地基环的大地测量中心点重合,这一偏差将影响设备对目标的测量精度,本文提出了一种能有效消除此偏差的方法.建立站点设备安装的回转中心定位公式,利用站点和方位标大地测量结果,经坐标变换重建设备回转中心的站址坐标和方位标数据,修正对中误差引起的设备对目标的测量精度影响.实际使用结果表明,此方法精度高、有效,且易于实施.     

Research into the effects of astronaut motion on the spacecraft: a review

The paper reviews the research that has been undertaken to understand and quantify the disturbance effects of the astronaut's motion inside and outside the spacecraft on the vehicle's attitude and acceleratory environment. In early investigations, the dynamic interaction of astronauts, modeled as point masses, and the spacecraft, modelled as a rigid body, was analyzed. Through ground-based experiments and the modeling of astronaut-induced forces and moments as stochastic processes, it became possible to estimate the magnitude and energy content of the loads produced by the astronaut. The first experiment in space to measure the astronaut-induced disturbances was conducted on the Skylab orbital station. Loads generated while performing routine operations were measured on board the Space Shuttle in 1994 and on the space station Mir in 1996–1997.     

The Motion of a Material Point in a Newtonian Field under the Action of Equiangular Thrust

The problems of investigation and optimization of the motion of spacecraft are extensively discussed in the literature. Nevertheless, in many cases a large variety of qualitative characteristics of their motion and of the form of their trajectories are still unclear. In this paper we consider a plane equiangular acceleration of a spacecraft both in a Newtonian field and in its absence (at a large distance from the center of attraction). The general equation of a trajectory of plane acceleration is presented with the introduction of a new variable, an index of an exponent, which allows one to obtain convenient solutions at different values of the time-independent angle of inclination of the vector of thrust to the spacecraft's radius vector (i.e., when equiangular acceleration takes place). Asymptotic solutions are constructed and an interesting fact is revealed. Namely, it is shown that when the center of attraction exists or is absent, for all initial conditions the trajectories appearing at the above equiangular acceleration of a material point tend to the standard logarithmic spirals at a large distance from the center. Specifically, when the value of transverse (perpendicular to the radius vector) thrust is constant, there appears a logarithmic spiral with an angle of inclination to the radius vector equal to 35.264°. Different forms of the trajectory of equiangular acceleration of spacecraft at a low thrust are also studied. The results obtained can be useful for the investigation and choice of optimum space trajectories.     

卫星双向时间频率传递中的Sagnac效应

 结合卫星双向时间频率传递技术,提出了在卫星运动情况下Sagnac效应解决方案。卫星双向时间频率传递技术是基于地球同步卫星进行的。地球同步卫星在各种摄动力的影响下,相对于地面上的某点不是绝对静止的,而是作小幅度日周期性运动。 Sagnac 效应与卫星和地面观测站的位置密切相关,卫星的运动直接导致了 Sagnac 效应也具有日周期变化的特征。使用高精度实测卫星轨道数据对 Sagnac 效应进行计算分析,结果表明：由卫星运动引起的Sagnac效应值具有与卫星运动一致的周日变化规律特征,大小达到几百皮秒的量级,与传统的将同步卫星作为静止点处理相比,提高了Sagnac效应误差的修正精度。该方案对于各种高精度卫星时间比对技术和卫星导航等领域具有重要的应用价值。