Motion parameters of an electrodynamic tether in orbit

The equilibrium states of an electrodynamic tether between two bodies of small mass in a near-polar orbit are studied. The behavior of the following parameters is traced during an astronomical day: tension of the tether, its radius of curvature, the angle of deviation from the orbital plane, induced electrodynamic force, etc. The lifetime of the tether in a circular near-earth orbit is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 111–121, March 2007.     

Deployment/retrieval optimization for flexible tethered satellite systems

A methodology for deployment/retrieval optimization of tethered satellite systems is presented. Previous research has focused on the case where the tether is modeled as an inelastic, straight rod for the determination of optimal system trajectories. However, the tether shape and string vibrations can often be very important, particularly when the deployment/retrieval speed changes rapidly, or when external forces such as aerodynamic drag or electrodynamic forces are present. An efficient mathematical model for flexible tethered systems is first derived, which treats the tether as composed of a system of lumped masses connected via inelastic links. A tension control law is presented based on a discretization of the tether length dynamics via Chebyshev polynomials. A scheme that minimizes the second derivative of length over the trajectory based on physically meaningful coefficients is presented. This is utilized in conjunction with evolutionary optimization methods to minimize the rigid body and flexible modes of the system during deployment/retrieval. It is shown that only a very small number of parameters are required to generate accurate trajectories. The results are compared to the case where the tether is modeled as a straight rod.     

航天器挠性梁伸展动力学特性数值分析

利用动量矩定理推导出带挠性伸展梁航天器的姿态动力学方程,推导了梁质量微元的动力学方程.在梁等速伸展的情况下对动力学方程进行变换,通过Runge-Kutta积分法得出了数值解.结果表明:梁等速伸展时,其振动的振幅随其长度的增长而增大;随航天器初始姿态角速率的增大而增大;随伸展速率的增大     

Modeling the motion of connected bodies

Spatial motion of mechanical systems consisting of jointed rigid bodies is considered. The methods previously developed to solve the dynamic equations of “carrier + loads” systems analytically for the accelerations of individual bodies are used to obtain the equations of motion of systems with complicated branched structure. The following practically important cases are analyzed: (i) a central carrier with peripheral loaded carriers and (ii) a chain and a ring consisting of loaded carriers. Numerical results are given for the stress-strain state of an elastic spacecraft represented as a chain of rigid bodies connected by elastic joints.     

Deployment of an orbital tethered system with an aerodynamic stabilizer

The control of an orbital tethered system (OTS) with an aerodynamic stabilizer (AS) is considered. The aerodynamic stabilizer is a light body of spherical shape with a relatively large ballistic coefficient. The system is deployed with the use of aerodynamic forces and with controlled braking by a special mechanism located on the main spacecraft (SC). A mathematical model describing the deployment and furthermotion of the OTS is constructed. The dynamic and kinematic control laws for the OTS deployment with and without feedback are analyzed. The influence of various disturbances on the stability of OTS deployment processes is estimated. An example where an aerodynamic stabilizer is used to ensure spacecraft descent from a low-earth orbit is given.     

飞行器角速度测量的三轴加速度计法

飞行器角速度的测量在航空航天领域是极为重要的问题,然而现在主流的利用陀螺仪测量角速度的方法有造价较高这一问题。本文提出了一种通过测量刚体上非共线三点的加速度得到刚体角速度的方法,可以利用极为廉价的高精度加速度计较为准确地测量高速稳态飞行器的角速度。本文应用刚体运动学中的基点法,得到由刚体上非共线三点的加速度和其距离表示的刚体角速度,并对其进行了误差分析。最终采用数值模拟的方法,分析了此方法在具有较高角速度的飞行器和具有较低角速度的稳态卫星上得到的角速度的适用性。模拟结果表明,此种方法适用于稳态高角速度的飞行器。     

Smoothing and statistical evaluation of laser Doppler velocimetry data of turbulent flows in rotating and reciprocating machinery

 Arbitrarily time-distributed velocity information acquired by laser Doppler velocimeter systems needs special care when evaluated wrt. the mean velocity and the components of the Reynolds stress tensor. In rotating machinery, the arrival time information can be uniquely mapped to the angular position ϕ of the runner blades by using encoder signals relating a fixed runner position to an arrival time. It is convenient to statistically evaluate the velocity information of the detected particles in an angular window [ϕ₀−Δϕ/2,ϕ₀+Δϕ/2] in order to obtain mean velocities and turbulence values for an angular position ϕ₀. This approach has the inconvenience that turbulence values calculated from standard deviations are influenced by a possible variation in the mean velocity in the evaluation window. Other problems that arise with this “evaluation window” method are the influence of unevenly angular-distributed velocity information on the mean velocity or the poor resolution of maxima and minima of the mean velocity, which is similar to the problem pointed out by Jakoby et al. but being of second-order nature. In this paper, different improvements in the “evaluation window” method wrt these problems based on ideas found in a paper by McDonald and Owen are presented. A confidence interval calculation, generalizing the methods of Boutier, for all calculated values is included, which allows an appropriate window size Δϕ to be chosen for each particular situation. The different methods are compared using examples from wake flows of axial hydraulic turbomachinery measured in air and water. Received: 7 July 1999/Accepted: 18 November 1999     

陀螺进动与强迫进动轨道

陀螺进动与轨道进动现象的相似性归因于二者的动力学相似性. 通过类比二者的动力学模型,提出了一类强迫进动轨道. 若以圆轨道为初始轨道,通过施加常值法向力可以实现一种特殊的悬浮型强迫进动轨道. 采用四元数建模方法求解了这种强迫进动轨道的进动规律,给出了解析表达式,据此分析了这种轨道的性质. 分析结果表明这种强迫进动轨道与初始圆轨道在同一球面上,且与初始位置相切. 其角速度为进动角速度与初始轨道角速度的合成,是一种悬浮轨道,即属于非开普勒轨道. 悬浮轨道在地球观测、行星际科学、天文观测、无线电通讯以及地球工程等领域具有潜在应用前景. 从强迫进动的角度出发所作的分析为悬浮轨道的实现提供了一种新途径.     

Review of deployment technology for tethered satellite systems

Tethered satellite systems (TSSs) have attracted significant attention due to their potential and valuable applications for scientific research. With the development of various launched on-orbit missions, the deployment of tethers is considered a crucial technology for operation of a TSS. Both past orbiting experiments and numerical results have shown that oscillations of the deployed tether due to the Coriolis force and environmental perturbations are inevitable and that the impact between the space tether and end-body at the end of the deployment process leads to complicated nonlinear phenomena. Hence, a set of suitable control methods plays a fundamental role in tether deployment. This review article summarizes previous work on aspects of the dynamics, control, and ground-based experiments of tether deployment. The relevant basic principles, analytical expressions, simulation cases, and experimental results are presented as well.     

多刚体系统分离策略及释放动力学研究

紧密连接的多刚体系统可在脱离运载航天器后在轨自主分离,无需多次利用航天器发射装置或在航天器中安装多个发射装置进行分离释放,从而有效提高运载航天器空间利用率,简化分离释放操作和降低碰撞风险.本文针对多刚体系统的在轨分离释放问题,研究在轨分离策略及释放过程动力学.首先,考虑刚体相对运动及姿态变化,基于虚功原理及自然坐标方法建立单个刚体的动力学模型.考虑多刚体系统在轨分离释放阶段的轨道运动和连接约束变化,计入分离时刚体间的相互作用,利用拉格朗日乘子法获得含连接约束的非线性动力学模型.考虑到实际工程应用,在多刚体系统分离释放阶段,通过安装在刚体间每个接触表面4个角上的弹射装置实现自主分离.其次,为保证分离过程中刚体之间无碰撞发生,规划了多刚体系统的分离时序,并基于不同弹射方向及分离顺序设计了两种分离释放方案.最后,通过算例研究分析了在轨分离释放过程中刚体的非线性动力学行为,验证了分离释放方案的有效性.     

Dynamic analysis of a tethered satellite system with a moving mass

This paper presents a dynamic analysis of a tethered satellite system with a moving mass. A dynamic model with four degrees of freedom, i.e., a two-piece dumbbell model, is established for tethered satellites conveying a mass between them along the tether length. This model includes two satellites and a moving mass, treated as particles in a single orbital plane, which are connected by massless, straight tethers. The equations of motion are derived by using Lagrange’s equations. From the equations of motion, the dynamic response of the system when the moving mass travels along the tether connecting the two satellites is computed and analyzed. We investigate the global tendencies of the libration angle difference (between the two sections of tether) with respect to the changes in the system parameters, such as the initial libration angle, size (i.e. mass) of the moving mass, velocity of the moving mass, and tether length. We also present an elliptic orbit case and show that the libration angles and their difference increase as orbital eccentricity increases. Finally, our results show that a one-piece dumbbell model is qualitatively valid for studying the system under certain conditions, such as when the initial libration angles, moving mass velocity, and moving mass size are small, the tether length is large, and the mass ratio of the two satellites is large.     

Mechanical problems in momentous projects of aerospace engineering

近年来, 我国航天重大工程蓬勃发展, 航天工程中新的力学问题不断涌现, 开展航天工程力学问题研究在航天技术的发展中起到举足轻重的作用.随着航天器朝着超高速、深空探测、多功能方向的发展, 其面临的发射和运行环境也更加恶劣, 发射过程中的多场耦合、非线性等问题更加突出. 大阵面、大挠性的航天器对在轨结构展开、模态辨识、刚柔耦合控制提出新的要求, 而高精度、高分辨率的观测需求, 为航天器在轨微振动、热致振动的研究带来了新的课题. 同时, 这一系列的问题也对航天器的地面试验和仿真分析等提出了更高的要求, 在这些领域, 各国学者也积累了一定的成果. 本文概括介绍了近年来航天重大工程中出现的新的力学问题, 从航天器的发射、在轨运行、地面仿真和试验等方面对航天工程中的力学问题进行了综述. 内容主要集中在耦合动力学、空气动力学、多体动力学、结构动力学以及试验力学等方面, 同时提出了工程中力学方面所面临的问题以及下一步的发展方向.     

航天重大工程中的力学问题

近年来,我国航天重大工程蓬勃发展,航天工程中新的力学问题不断涌现,开展航天工程力学问题研究在航天技术的发展中起到举足轻重的作用。随着航天器朝着超高速、深空探测、多功能方向的发展,其面临的发射和运行环境也更加恶劣,发射过程中的多场耦合、非线性等问题更加突出。大阵面、大挠性的航天器对在轨结构展开、模态辨识、刚柔耦合控制提出新的要求,而高精度、高分辨率的观测需求,为航天器在轨微振动、热致振动的研究带来了新的课题。同时,这一系列的问题也对航天器的地面试验和仿真分析等提出了更高的要求,在这些领域,各国学者也积累了一定的成果。本文概括介绍了近年来航天重大工程中出现的新的力学问题,从航天器的发射、在轨运行、地面仿真和试验等方面对航天工程中的力学问题进行了综述。内容主要集中在耦合动力学、空气动力学、多体动力学、结构动力学以及试验力学等方面,同时提出了工程中力学方面所面临的问题以及下一步的发展方向。     

多储液腔航天器刚液耦合动力学与复合控制

采用复合控制方法对充液航天器的姿态和轨道机动进行高精度控制.通过傅里叶-贝塞尔级数展开法,将低重力环境下液体的弯曲自由表面的动态边界条件转化为简单的微分方程,其中耦合液体晃动方程的状态向量由相对势函数的模态坐标和波高的模态坐标组成.通过广义准坐标下的拉格朗日方程得到航天器刚体部分运动和液体燃料晃动的耦合动力学方程,提出了自适应快速终端滑模策略和输入整形技术相结合的复合控制器,并分别用于控制携带有一个燃料腔和四个燃料腔航天器的轨道机动和姿态机动.通过数值模拟来验证控制器的效率和精度.结果表明,对于多储液腔航天器,如果在设计航天器的姿态和轨道控制器时没有充分考虑燃料晃动效应,那么在受控航天器系统中将会出现刚-液-控耦合问题并导致航天器姿态不稳定.而本研究中的复合自适应终端滑模控制器可以实现航天器机动的高精度控制并有效抑制液体燃料晃动.     

带脉冲的三维引力辅助变轨研究

在引力辅助过程中施加脉冲可以有效地改善变轨效果.目前只能对施加小脉冲的情况进行近似计算,当脉冲大于近拱点速度的1%时无法进行分析.针对这一问题,提出了一种解析分析方法,可以计算施加任意大小和方向脉冲的三维引力辅助变轨.基于二体问题,建立了带任意脉冲的三维引力辅助模型,采用8个相互独立的参数对模型进行描述,其中5个参数表征三维引力辅助、一个参数表征脉冲的大小、两个参数表征脉冲的方向;建立了一组坐标系,可以方便地对轨道进行描述;以施加脉冲为界,将轨道划分为前后两段,分别进行公式推导;应用双曲线轨道动力学与坐标变换等技术方法,可以将飞行器的位置矢量和速度矢量表示为上述8个参数的解析公式,进而可以求出变轨导致的速度、能量和轨道倾角的变化量.通过与基于圆型限制性三体问题的数值仿真结果进行对比,验证公式的有效性.应用导出的解析公式分析了施加脉冲的大小和方向对飞行器能量和轨道倾角的影响,并给出了相应规律.结果表明:以最大能量改变为优化目标,施加脉冲的最优方向往往并不是该点速度方向;轨道倾角受到脉冲方向的影响显著.      

Chaotic pitch motion of an asymmetric non-rigid spacecraft with viscous drag in circular orbit

We study the pitch motion dynamics of an asymmetric spacecraft in circular orbit under the influence of a gravity gradient torque. The spacecraft is perturbed by a small aerodynamic drag torque proportional to the angular velocity of the body about its mass center. We also suppose that one of the moments of inertia of the spacecraft is a periodic function of time. Under both perturbations, we show that the system exhibits a transient chaotic behavior by means of the Melnikov method. This method gives us an analytical criterion for heteroclinic chaos in terms of the system parameters which is numerically contrasted. We also show that some periodic orbits survive for perturbation small enough.     

Efficient approaches of determining the motion of a spherical particle in a swirling fluid flow using weighted residual methods

The motion of a spherical particle released in a swirling fluid flow is studied employing the least-squares method and method of moments. The governing equations are obtained and solved employing the two methods. The accuracy of the results is examined against the results of a fourth-order Runge–Kutta numerical method. The effects of various parameters, namely the initial radius, initial radial velocity, initial angular velocity, and drag-to-inertia ratio, on the non-dimensional velocity profiles and particle position distribution are considered. The results show that the radial velocity increases over time while the angular velocity decreases, and that an increase in the initial radial velocity increases the particle radial distance and angular velocity but decreases the radial velocity profile.     

An analytical control law of length rate for tethered satellite system

Based on the nonlinear dynamic equations of a tethered satellite system with three-dimensional attitude motion, an analytical tether length rate control law for deployment is derived from the equilibrium positions of the system and the scheme of the value range of the expected in-plane pitch angle. The proposed control law can guarantee that the tensional force acting on the end of the tether remains positive. The oscillation of the out-of-plane roll motion in conjunction with the in-plane pitch motion is effectively suppressed during deployment control. The analytical control law is still applicable, even if the system runs on a Keplerian elliptical orbit with a large eccentricity. The local stability of the non-autonomous system during deployment control is analyzed using the Floquet theory, and the global behavior is numerically verified using simple cell mapping. The numerical simulations in the paper demonstrate the proposed analytical control law.     

Dynamics of body separation—analytical procedure

In this paper, an analytical procedure for the determination of the dynamic parameters of a remainder body after mass separation is developed. The method is based on the general principles of momentum and angular momentum of a body and system of bodies. The kinetic energy of motion of the whole body and also of the separated and remainder body is considered. The derivatives of kinetic energies with respect to the generalized velocity determine the velocity and angular velocity of the remainder body. To confirm the proposed procedure, the results are compared with those obtained using the method of momenta and angular momenta. In the paper, the theorem about increase of kinetic energies of the separated and remainder bodies for perfectly plastic separation is proved. The increase of the kinetic energies correspond to the relative velocities and angular velocities of the separated and remainder bodies. As an example, the mass separation from a pendulum is considered. The kinematic properties of the remainder pendulum are obtained using the analytic procedure. The results are in agreement with those obtained by applying the basic principles of Newton’s mechanics.     

Analysis of attitude motion evolutions of variable mass gyrostats and coaxial rigid bodies system

This work involves the research into angular motion of variable mass gyrostats, coaxial bodies systems and dual-spin spacecraft in a translating coordinate frame. The variability of mass-inertia parameters of coaxial bodies causes non-trivial changes of system angular motion. The article describes qualitative method for phase space analysis, based on the evaluation of a phase trajectory curvature. The method can be used to investigate the phase trajectory shape and to synthesize conditions for special motion modes realization (for example, monotone decreasing/increasing of nutation angle). The paper results can be used to describe the motion of a variable mass dual-spin spacecraft, performing active maneuvers.