Stabilization of a Reentry Vehicle by a Partial Spin-up during Uncontrolled Descent

Stabilization of a reentry vehicle (RV) by a partial spin-up of it is considered for the case of uncontrolled descent into the atmosphere. In this case, the vehicle is a composite construction consisting of two rigid bodies, a return capsule and a stabilizing block, which is put in rotation. A model is developed for the spatial motion of the reentry vehicle considered as a system of coaxial rigid bodies rotating about a common axis of symmetry. The free motion is studied, and the stability of steady-state regimes is analyzed. The spatial motion of the system is considered for the case of a small asymmetry due to displacement of the axes of dynamic symmetry of the bodies with respect to the spin axis, and approximate solutions for the motion parameters of the free system are found.     

Analysis of the dynamics of the deployed aerodynamic space tether system

An analysis of the motion of a deployed space system that consists of two end bodies connected by a tether has been considered. One of the bodies has a relatively large ballistic coefficient that ensures aerodynamic braking or the stabilization of the motion of the entire system in relatively low near-Earth orbits. The deployment of this system mainly occurs due to the action of aerodynamic forces. Several ways of deploying the system have been analyzed, including (1) the uncontrolled release of the tether with hardly any braking; (2) deployment with constant braking force; (3) the dynamic control law without feedback, when the resistance force varies according to a set program; (4) a kinematic control law with feedback when programs are set for varying the velocity and length of the tether release. To analyze the dynamics of the system, a mathematical model of motion has been constructed in which the motion of the end bodies relative to their centers of mass is taken into account.     

Optimum parameters of a gravitational satellite-stabilizer system

Dynamics of a satellite-stabilizer system is studied. It is supposed that there is a viscous friction in a hinge connecting two bodies, but there is no elasticity. The attitude motion in a plane of circular orbit is considered, and parameters are determined, at which natural oscillations near a stable equilibrium position in the orbital coordinate system are damped out most rapidly. The rate of transient processes is estimated by a value of the degree of stability of linearized equations of motion. The optimization of the degree of stability is sequentially performed in dimensionless damping coefficient (the first stage) and in inertial system parameters (the second stage). The result of the first stage is the partition of system parameter space into the regions, in each of which the maximum of the degree of stability is reached on a particular configuration of roots of the characteristic equation. It is shown at the second stage that the global maximum is reached at two points of parameter space, where one of system bodies degenerates into a plate, and the characteristic equation has four equal real roots.     

Planar inertial motion of an elastic cluster of three bodies

A problem of planar inertial motion of three bodies connected in the form of a triangle by an elastic imponderable filament is considered, as well as a particular case of the problem of motion of a closed chain of n bodies. This configuration can be a basis for extended planar constructions in deep space.The bodies are considered as material points. The paper elaborates a subject of [1]     

The use of a movable telescoping end mass system for the time-optimal control of spinning spacecraft

The time-optimal control of a spin-stabilized spacecraft with a movable telescoping appendage (boom), is considered analytically and numerically. The motion of a control mass at the end of the boom is determined such that the terminal time will be minimized for two-axis control of a symmetric spacecraft. The equations of rotational motion are linearized about the desired state of spin about the symmetry axis. The equations for the transverse angular velocity components have the form of a coupled two dimensional harmonic oscillator with boom motion as a control force. The control function which brings the system to the desired state is known to be a series of positive and negative pulses. If the initial state is such that the system can be driven to rest in a single switch, the responses, switching and final times, and required boom motion may be determined analytically. Some typical numerical results based on these solutions are discussed.     

空间机械臂建模方法与控制策略研究

针对刚柔耦合空间机械臂动力学建模中对柔性体采用的传统描述方法（有限元法、模态综合法以及集中参数法等）并不足以精确描述柔性大变形的问题,采用绝对节点坐标法描述柔性体,采用自然坐标法描述刚性体,建立了末端带集中质量的双连杆柔性机械臂的动力学模型并且研究了机械臂的空间定位问题。结合广义α法以及工程上常用的Scaling技术,开发了计算程序,实现了动力学方程的高效精确数值求解。针对机械臂的空间定位以及柔性变形问题,提出了一种运动规划方案,采用PD控制策略,实现了机械臂的运动跟踪控制;仿真结果表明：提出的运动规划方案能有效地减弱机械臂的柔性变形。     

Equilibrium positions of a weight on a cable fixed to a dumbbell-shaped space station moving along a circular geocentric orbit

The motion of a space object in the gravitational field of the Earth is considered. The object consists of an extended space station and a weight, which is free to move along the cable fixed to the ends of the station. It is assumed that the station is composed of two masses coupled by a weightless rod, while the cable is weightless and non-stretched. The equations of motion of such a system are derived for the case when the motion proceeds in a single plane, while the center of mass of the system moves along a circular geocentric orbit. The conditions of the cable tension (conditions of being on tie) are derived. The phase portrait of the weight motion along the cable is constructed when the station is oriented to the attracting center or is perpendicular to this position. The possibility to leave the tie in this case is analyzed. Equilibrium configurations of the system are found, i.e., such motions of the object under consideration at which the weight does not change its position relative to the station. Lyapunov stability of such configurations is analyzed for two situations: when the station is composed of equal masses and when masses at the ends of the station are different. In particular, for the case of different masses it is established that there exist such positions of equilibrium at which the dumbbell is located at an angle to the direction to the attracting center. In some cases these positions can be stabilized (if the weight is fixed on the cable).     

含板类柔性附件的充液航天器动力学研究

对含有板类柔性附件和曲壁轴对称充液储腔的复杂航天器系统进行动力学建模和耦合机理研究。首先,采用Kirchhoff-Love薄板理论对航天器的板类柔性附件进行研究,通过D’Alembert原理得到柔性附件的振动方程,运用模态假设法将混合方程转换为常微分方程。其次,通过推导充液航天器储腔内任意点的运动,得到储腔液体的牵连速度势函数,采用Gauss超几何级数得到液体相对速度势函数的解析形式,通过Hamilton变分原理推导液体晃动的运动方程,以及液体速度势函数模态系数的控制方程。最后采用准坐标Lagrange方程得到耦合航天器系统的状态方程,通过数值仿真校验系统动力学模型的有效性。研究结果表明,刚性平台、液体、柔性附件的相互耦合效应使得航天器系统存在复杂动力学行为,在复杂航天器系统动力学建模过程中需要充分考虑液体晃动和柔性附件振动的影响,柔性附件的安装位置对于耦合航天器系统的动力学行为也有着重要影响。     

The Motion of Coaxial Bodies of Varying Composition on the Active Leg of Descent

The motion of a spacecraft (SC) with double rotation and variable mass on the active leg of its descent is considered. The SC consists of two coaxial bodies. The coaxial scheme is used for gyroscopic stabilization of the SC longitudinal axis by the method of partial spin-up. The equations of spatial motion of coaxial bodies of varying composition are derived and approximate solutions for the angles of spatial orientation are found. The condition of decreasing amplitude of nutation oscillations is obtained, which allows the estimation of efficiency of the stabilization by partial spin-up. The errors in the magnitude and direction of the vector of braking thrust are also determined.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 3, 2005, pp. 224–232.Original Russian Text Copyright © 2005 by Aslanov, Doroshin, Kruglov.     

General dynamics of a large class of flexible satellite systems

The paper presents a general formulation for librational dynamics of satellites with an arbitrary number, type and orientation of deploying flexible appendages. In particular, the case of beam-type flexible appendages deploying from a satellite in an arbitrary orbit is considered. The governing nonlinear, nonautonomous and coupled equations for vibration of the appendages and libration of the satellite are integrated numerically. Several cases of practical importance are considered making the system progressively more general and hence complex: (i) planar case representing pitch and appendage oscillations in the orbital plane; (ii) general attitude motion with planar vibrations of flexible members; (iii) above two cases together with the out-of-plane component of vibrations. Results show that under critical combinations of the system parameters the combined effect of flexibility and deployment can be substantial.     

Evolution of motion of two viscoelastic planets in the field of forces of their mutual attraction

Translational-rotational motion of two viscoelastic planets in a gravitational force field is studied. The planets are modeled by homogeneous isotropic viscoelastic bodies. In their natural undeformed state each of the planets represents a sphere. We investigate a specific case when the planet’s centers of mass move in a fixed plane, the axis of rotation for each planet being directed along the normal to this plane. An equation describing the evolution of a slow angular variable (perihelion longitude) is derived. The observed displacement of the perihelion of Mercury is compared with the results obtained in the considered model problem about motion of two viscoelastic planets. Quite important is the fact that the planet of smaller mass (Mercury) moves not in a central Newtonian field of forces, but rather in the gravitational field of a rotating viscoelastic planet (Sun).     

Optimization of passive orbit with the use of gravity maneuver

A high-precision method of calculating gravitational interactions is applied in order to determine optimal trajectories. A number of problems, necessary for determination of optimal parameters at a launch of a spacecraft and during its flyby near celestial bodies, are considered. The spacecraft trajectory was determined by numerical integration of the equations of passive motion of the spacecraft and of the equations of motion for planets, the Sun, and the Moon. The optimal trajectory of the spacecraft approaching the Sun is determined by fitting its initial conditions.     

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].     

On analysis of close encounters of two cosmic bodies in near almost-circular orbits

This paper is devoted to the study of relative motion and close encounters of two cosmic bodies located in near almost-circular orbits. This problem is topical due to the asteroid hazard proceeding from the NEA group asteroids located in the near-Earth orbits. The (99942) Apophis asteroid, a representative of this group discovered in July 2004 by the Kitt Peak observatory (Arizona), is considered as an example.     

Motion of a Planet with a Complex Structure

The motion of a planet consisting of a mantle and a core (solid bodies) connected by a viscoelastic layer and interacting with each other and an external point mass by the law of gravitation is considered. The mutual motions of the core and mantle are investigated assuming that the centers of mass of the planet and external point mass moves along undisturbed Keplerian orbits around the common center of mass of the system. The planetary core and mantle have an axial symmetry and different principal moments of inertia, which leads to a displacement of the center of mantle relative to the center of core and to their mutual rotations. The results obtained on the basis of averaged equations are illustrated by the example of the Earth–Moon system.     

Chaos and its avoidance in spinup dynamics of an axial dual-spin spacecraft

Attitude dynamics of a dual-spin spacecraft (DSSC) and a torque-free angular motion of a coaxial bodies system are considered. Some regimes of the heteroclinic chaos are described. The local chaotization of the DSSC is investigated at the presence of polyharmonic perturbations and small nutation restoring/overturning torques on the base of the Melnikov method and Poincaré Maps. Reasons of the chaotic regimes initiation at the spinup maneuver realization are studied. An approach for the local heteroclinic chaos escape/avoidance at the modification of the classical spinup maneuver is suggested.     

Ballistics of a fragmenting meteor body with allowance made for ablation in the non-isothermal atmosphere. II

The second part of the work is devoted to studying the motion of fragmenting meteor bodies with ablation by fragments in a planet’s atmosphere, taking into account its non-isothermal character in altitude. The mechanical fragmentation of a meteoroid under the action of aerodynamic drag is considered in the context of statistical strength theory. An analytical solution for ballistics of a fragmenting body is obtained at a constant parameter of ablation. A theoretical analysis of the derived regularities is made and an example of their usage in the problem of a comet-asteroid hazard is presented.     

A Proposal for Constructing a Group of Space Objects for Solving Transport and Energy Problems

We propose to develop a scheme for a group of space objects which includes a set of orbital tethers and exchange masses. These objects are injected into circumterrestrial orbits. A variety of problems can be solved with the help of this space system, namely, transport problems and problems of converting the electric power generated onboard spacecraft into mechanical energy of motion of the space objects. In the future, natural celestial bodies (in particular, the Moon) can be considered as elements of the system. This opens up the possibility of using the energy of motion of the Moon both for solving transport problems and for generating electric power onboard spacecraft.     

绳系卫星系统的运动与控制

绳系卫星系统的运动与控制分析,是绳系卫星应用的基础。本文的数学模型考虑了作用在子星、主星及系绳上的空气阻力以及在伸展与收回阶段主星与系绳之间的质量传递,给出了相应的具体的计算式。应用该数学模型,本文对现有的几种主要控制法,进行了模拟计算,作出评审意见。