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.     

空间绳系机器人抓捕非合作目标的质量特性参数辨识

针对空间绳系机器人抓捕非合作目标/空间垃圾后需要对其进行回收/拖曳的精确控制问题,提出了一种利用抓捕后保持阶段的振动特性辨识目标参数的方法。首先,根据质量特性参数辨识的需要,推导了系统的动力学模型。不同于以往将本体卫星和被抓捕目标简化为质点的动力学模型,本文针对任意的目标抓捕位置,在考虑重力梯度影响的基础上,利用拉格朗日法获得系统各广义坐标的动力学公式。然后,分析非合作目标和系绳在后抓捕保持阶段的姿态运动。最后,在非合作目标与本体卫星没有任何信息交互的情况下,利用后抓捕阶段目标卫星和系绳特有的振动,并使用具有鲁棒性可遗忘因子的递推最小二乘法,提出了包括转动惯量和质心到任意抓捕点距离在内的质量特性参数辨识算法。     

The fluid-dynamic disturbances induced on the ISS, based on the first acceleration measurements on board the space station

The different acceleration components on the ISS that are responsible for the generation of convective motions in a fluid cell either in the presence of density gradients or in quasi-isodense processes, are analyzed. The NASA measurements of the quasi-steady and periodic acceleration on the ISS are considered and their effects on fluid-dynamic experiments are computed and discussed under different assumptions. In particular, numerical simulations are carried out to identify the relative importance of linear and pendular accelerations, due to possible rotations of the P/L around its center of mass. The effects caused by variable accelerations created by an isolation mount that exhibits an attenuation factor not constant within the payload volume, caused by the reaction forces of the umbilicals, are computed and analyzed.     

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.     

On optimal aerodynamic attitude control of spacecraft

Attitude control of spin-stabilized satellites by means of aerodynamic forces is investigated. A controller employing two rotatable control surfaces is proposed to control the roll-yaw motions of the spacecraft spin-axis. Optimal control theory is applied to synthesize a feedback control law for the control surface rotations which leads to asymptotically stable controller operation. The system response is interpreted in terms of performance criteria such as the maximum control surface excursions, the speed of response and the associated orbital energy loss due to drag. Even with a moderate size, the controller appears quite effective in maintaining the spacecraft attitude against external disturbances.     

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.     

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.     

航天器集群构形控制的虚拟弹簧阻尼网络方法

针对航天器集群质心相对运动构形控制问题,提出了一种基于虚拟弹簧阻尼网络的分布式控制方法。航天器间以虚拟的弹簧阻尼器相互连接,弹簧的原长根据期望的相对运动构形来设定。各航天器的控制输入是与其相连的所有弹簧阻尼器的合力。在线性动力学模型和拓扑结构连通且固定的假设下,基于代数图论的方法推导出了闭环系统稳定性条件。对近地轨道上100个航天器形成格点相对运动构形和20个航天器形成时变距离的椭圆构形的实例进行了仿真,考虑了轨道摄动的影响,结果表明,集群通过虚拟弹簧阻尼网络控制可实现期望构形,并能达到厘米量级的构形保持控制精度。该控制方法不改变集群的质心,只需施加很小的控制加速度;仅基于局部的邻居交互,能够适应大规模集群对分布式控制的要求。     

Periodic motions of a satellite-gyrostat relative to its center of mass under the action of gravitational torque

We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.     

带多充液圆柱贮箱航天器刚-液耦合动力学研究

文中以在低重环境下带多充液圆柱贮箱刚性航天器中刚-液耦合方程的建立和求解为主要研究目的。推导航天器中充液圆柱贮箱内任意点的牵连运动方程,根据壁面边界条件给出了贮箱内液体牵连晃动势的表达式;利用第二类边界条件下的傅立叶-贝塞尔级数展开法对低重力环境下的弯曲自由液面处的复杂动力学边界条件进行处理,建立以液体相对晃动势的模态坐标和晃动波高的模态坐标为状态向量的液体耦合晃动力学方程,通过积分分别得到了耦合晃动力和耦合晃动力矩的解析式;运用准坐标系下的拉格朗日方程建立以航天器主刚体姿态坐标和轨道坐标为状态向量的刚体耦合运动动力学方程,进一步联立上述耦合方程得到航天器整体系统的刚-液耦合动力学状态方程;最后,编制出适用于带多充液圆柱贮箱航天器内刚-液耦合动力学计算的模块化计算程序,通过计算实例验证所编程序的准确性的同时,研究了携带多充液箱航天器系统贮箱布局、外激励方式对航天器刚-液耦合系统动力学特性的影响。     

Regularization of the Limit Problem of Satellite Librations in a Keplerian Orbit Taking Light Pressure into Account

The planar librations of a satellite whose center of mass moves along an elliptic orbit are considered. It is assumed that not only the gravitational moment but also the forces of light pressure act upon the satellite. Account is taken of the fact that the right-hand sides of the differential equations are nonanalytic functions of the phase variables. When e 1, e being the orbit's eccentricity, the deformations of solutions are considered for the case of a satellite moving along a highly elongated orbit. Such transformation of the initial system of differential equations is carried out so that the new system becomes regular up to the value e = 1. A limit problem corresponding to the case e = 1 is considered. When the azimuth angle of the light source coincides with the direction to the pericenter, the dynamical system is reversible. In this case, the known families of the periodic solutions to the problem can be continued up to the limit case.     

Equivalent mechanical model for liquid sloshing during draining

For a spacecraft draining liquid fuel during a continuous thruster maneuver, a brief equivalent method is proposed to model the time-varying properties of liquid sloshing for dynamics and control design. The sloshing liquid during draining is equivalent to a set of mechanical model with variable parameters. The model parameters for sample filling ratios are determined by an efficient finite element method according to equivalent principles, while the parameters for other filling ratios are obtained by piecewise linear interpolation. Using the proposed model, forces and torques acted on a Cassini shaped tank by the inside liquid during draining are investigated undergoing several typical motions. Verifications and comparative studies are done with Computational Fluid Dynamics simulations, which confirm the accuracy of the brief model while the sloshing amplitude is small and the flow rate is low.     

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.     

On the stability of stationary motions of a system of coaxial bodies

We consider the stability of stationary motions of a model of a spacecraft as a system of coaxial bodies with small asymmetry caused by the shift of the axes of dynamic symmetry of bodies relative to the axis of rotation. We determine the stationary motions of the system; their stability is studied with respect to both the projections of angular velocity and the position of the axis of rotation. The sufficient conditions for the stability of these stationary motions are obtained by constructing a Lyapunov function, and the necessary conditions are obtained by analyzing the corresponding linearized equations of perturbed motion.     

Resonance Effects when Moving a Small Spacecraft around the Center of Mass in a Deployable Tether System

Cosmic Research - The resonance motions of a small spacecraft relative to the center of mass when deploying a tether system are analyzed. The tether system is deployed from a base spacecraft moving...     

Nonlinear deformation of a longitudinally corrugated shell structure with uniform load

In this paper, we study the nonlinear deformation of a longitudinally corrugated shell (a type of morphing structure) with a uniform load. We derived the governing equations of the deformations of that corrugated shell with Nayfeh and Pai's [1] initial curvature of shell geometries and developed numerical solutions for that nonlinear mechanics problem. This numerical method is extremely efficient since no element discretization is implemented. The obtained solutions can be verified by comparing with the analytical solution for the same structure with infinitesimal strains. Furthermore, we apply the present method to study a cylindrical shell under the uniform internal pressure, and find that the displacements and internal forces of the cylindrical shell agree well with results obtained from von Kármán nonlinear shell theory. Finally, from parametric studies, we can figure out that the increment of the percentage of the arc part and the total length of the corrugated ring can increase the expansion and internal forces of the corrugated ring. And the configuration of the corrugated ring are more sensitive to the change of geometry and material parameters than internal forces, which indicate that the morphing function can be realized through the change of geometry and material parameters of the structure without great change in the maximum internal forces of the ring. By comparing the results from present nonlinear theory with those from linear theory, we can also find that the displacements and internal forces obtained from linear shell theory can either be exaggerated or disguised for the different configurations of the ring.     

The motion of a synchronous satellite in a system similar to the earth-moon system

The stationary motions of a synchronous axisymmetric satellite are studied in the field of attraction by the Earth and a third body whose parameters are close to those of the Moon. Equations of motion are written in canonical variables that take into account the resonance character of the problem. The plots characterizing the dependence of the rotation parameters of the satellite relative to the center of mass on the elements of satellite’s translational motion are presented. A picture is given that represents the initial configuration of the system for implementing stationary motions.     

一类柔性宏刚性微空间机器人广义动力学高效率建模研究

研究了一类柔性宏刚性微空间机器人广义高效递推动力学建模算法。介绍了利用空间 算子代数进行对刚柔混合欠驱动系统的描述方法。根据系统中铰链的驱动情况分别对铰链定 义 为主动铰和被动铰,通过铰链的类型以及判断是刚性体或者柔性体,分别按照两次从系统的 顶端到基座的顺序、一次从基座到顶端的顺序进行了系统铰接体惯量的递推、系统冗余力的 递推、广义加速度和广义主动力的递推。通过上述三种方式的递推过程建立了柔性宏刚性微 空间机器人广义递推动力学模型,实现了高效率O（n）次的计算效率。最后通过软 件仿真验证了本研究内容的正确性和高效性。
     

Evolution of Motion of a Binary Planet

A model of a binary planet, consisting of a material point of small mass and a deformable viscoelastic sphere, is suggested. The center of mass of the binary planet moves in the gravitational field of a central body in the plane, which contains planets forming the binary planet. A deformable spherical planet rotates around the axis orthogonal to the plane of planetary motion. Planet deformations are described by the linear theory of viscoelasticity. It is shown that with an appropriate approximation of the gravitational potential, there is a class of quasicircular orbits, when the eccentricities of an orbit of the center of mass of a binary planet and an orbit, describing mutual planet motion, are equal to zero. The further evolution of motion is investigated in this class of orbits with the use of the canonical Poincare–Andoyer variables. Corresponding averaged equations are found, and phase pictures are constructed; the stability of stationary solutions is investigated on the basis of equations in variations. For the Solar system planets with their satellites, forming binary planets, the application of the presented model allows us to conclude that satellites sooner or later will fall on the corresponding planets.     

光学稳像系统颤振抑制性能的分析与设计

光学稳定成像方法是一种用于隔离视轴颤振对成像质量影响的综合处理技术,它结合传统光学与反馈控制理论,通过闭环控制系统驱动在光成像通路内的动态校正机构补偿探测视轴与成像焦面间的相对运动,进而有效提升成像质量。文章首先建立了光学稳像系统的回路模型,并在此基础上,根据控制系统稳定性判据导出了颤振抑制函数的设计约束,分析了像移测量延时特性、测量精度特性及校正机构动态性能对颤振抑制带宽的影响。文章进一步给出了一种光学稳像系统颤振抑制带宽的设计方法,该方法针对视轴颤振的功率谱密度、像移探测性能和光机校正机构的动态性能完成了颤振抑制带宽的优化,从而可最小化颤振补偿残差。最后通过试验验证了文中分析结论和设计方法的有效性。