Gravitational and hydroelastic waves in thomson-delaney cells of the ocean on Jovian Moon Europa

The possibility of appearance of hydrothermal cells in the system “Ocean of Jovian Moon Europaits ice crust” was theoretically proved by R. Thomson and J. Delaney [8]. We formulated in [11] boundary value problems for planetary gyroscopic waves and gravitationally elastic waves in these cells, and the spectrum of nondivergent gyroscopic waves was numerically investigated. The present paper is a continuation of [11]. It considers the spectra of independent, purely gravitational and hydroelastic waves. The possibility of resonant excitation in Thomson-Delaney cells of gravitational and hydroelastic waves is considered.     

柔性多体航天器单向递推组集建模方法

本文提出一种面向计算机建立柔性多体航天器动力学方程的新方法，其特点是完成运动学正向递推同时实现动力学方程的组集。这种方法不仅可提高航天器、空间机械臂动力学仿真的计算效率，而且可有效地克服数值积分病态的困难。文末一个空间四杆柔性机械臂的算例验证了这种建模方法的上述优点。     

压电层合板壳的数值分析与控制仿真

从虚功方程出发,推导出具有压电传感器和驱动器的层合板壳的机电耦合动力方程,建立了新的压电固体单元以模拟压电层合结构的力学特性和振动控制。通过引入EAS模式,代替通常采用的增加非协调函数的办法克服模拟薄板时所遇到的过高剪切应变能的缺陷,从而明显减少了内部变量的个数,提高了计算效率;进而在厚度方向上增加一个线性分布的横向应变,克服了用于壳体结构的分析时所遇到的厚度自锁问题;提出了一个新的电势插值函数,大大减少了电自由度的个数,显著降低了数据读取、存储和凝聚电自由度的计算花费。数值算例表明,推导的单元适用于薄壳结构的数值分析,并具有很好的对歪斜网格的适应性。     

压电框架单元及其在结构振动控制中的应用

重点阐述了含坟电传感器和执行器的复合结构框架有限元模型的建立过程，导出了压电框架单元的压电刚度矩阵和介电刚度矩阵，进而引入基本控制规律用数值例子说明了压电传感器与执行器在结构的振动控制中的具体应用。     

Transient attitude dynamics of satellites with deploying flexible appendages

The paper presents a general formulation for librational dynamics of satellites with an arbitrary number, types, and orientation of deploying flexible appendages. The generalized force term is incorporated making the formulation applicable to a wide variety of situations where aerodynamic forces, solar radiation, earth's magnetic field, etc. become significant. In particular, the case of a beam-type flexible appendage deploying from a satellite in an arbitrary orbit is considered. The corresponding nonlinear, non-autonomous equations for in-plane and out-of-plane vibrations are derived, allowing for the variation of mass density and flexural rigidity along the length with time dependent deployment velocity and spin rate. Next, the attention is focused on the linearized analysis of the in-plane vibrational equation using the assumed-mode method and its substantiation through numerical integration. Finally, the paper presents results for both steady-state and transient attitude behaviour for a representative gravity gradient configuration for a range of initial conditions and system parameters. Results show the combined effect of flexibility and deployment on the dynamics of the system to be substantial. Disturbance of the appendage can excite large amplitude librations. On the other hand, the converse situation is not necessarily true. Furthermore, Coriolis loading, induced by the extending appendages, can become a limiting factor in arriving at a deployment strategy; an effect not pointed out in the literature.     

Control-structure interaction study of the proposed space station freedom

A relatively general formulation for studying the dynamics and control of an arbitrary spacecraft with interconnected flexible bodies has been developed accounting for transient system properties, shift in the center of mass, shear deformations, rotary inertias and geometric nonlinearities. This self-contained, comprehensive, numerical algorithm using system modes is applicable to a large class of spacecraft configurations of contemporary and future interests. Here, versatility of the approach is demonstrated through the dynamics and control studies aimed at the evolving Space Station Freedom.     

Numerical modelling of the interface conditions in coupled marangoni flows

The implementation in numerical codes of the coupling conditions between bulk phases adjacent to an interface exhibiting Marangoni effect is examined. The conditions are detailed in the case of a vorticity, stream-function, temperature formulation of the field equations. Numerical examples are reported for particular cases.     

Analysis of spacecraft motion under constant circumferential propulsive acceleration

This paper reassesses the classical circumferential-thrust problem, in which a spacecraft orbiting around a primary body is subjected to a propulsive acceleration of constant modulus, whose direction is in the plane of the parking orbit and orthogonal to the spacecraft-primary line. In particular, a new formulation is proposed to obtain a reduction in the number of differential equations required for the study of the spacecraft propelled trajectory. The mathematical complexity of the problem may be further reduced assuming that both the propulsive acceleration modulus and the spacecraft distance from the primary body are sufficiently small. In that case, an approximate model is able to accurately describe the characteristics of the propelled trajectory when the parking orbit is circular. Finally, using the data obtained by numerical simulations, the approximate model is extended to generate a set of semi-analytical equations for the analysis of a classical escape mission scenario.     

基于迭代修正方法的严格回归轨道设计

通过分析太阳同步回归轨道的轨道根数和星下点经度/纬度的关系,推导了一组轨道根数的修正公式。基于高精度轨道动力学模型和升交点位置确定方法,构造了关于轨道半长轴和轨道倾角的迭代修正方法。针对偏心率矢量的动力学系统所具有的极限环特性,构造了平均法求其解析近似,从而实现冻结轨道特性对偏心率和近地点幅角的迭代修正。结合迭代修正,得到一组严格回归的轨道根数。该轨道能够重访空间目标点,具有较高的回归精度。     

用样条有限点法分析梁和薄板的弹塑性弯曲

本文首次用样条有限点法(SFPM),分析了梁和薄板的弹塑性弯曲,并给出了计算实例。通过计算表明:SFPM具有方法简单、节约内存、计算精度高等优点。对于规则区域的特殊问题,SFPM做为有限元法的一种补充,是一种有效的数值分析方法。     

激光等离子体天线的电磁散射分析

根据激光等离子体天线工作原理给出了电磁分析模型,以电场作为未知函数建立了频域体积分-微分方程,用脉冲基函数和点匹配函数的矩量法（MOM）将之转为线性代数方程组。求解中应用快速傅里叶变换（FFT）和共轭梯度法（CGM）,以降低所需计算机内存和减少CPU计算时间。算例表明：该法计算的结果与Mie级数解析解和其他文献结果吻合较好。     

绳系空间太阳能电站动力学响应分析

利用绝对节点坐标方法研究绳系空间太阳能电站在轨飞行的太阳能电池板动力响应。通过勒让德变换引入广义动量,在约束哈密尔顿体系下建立轨道、姿态和弹性振动耦合的动力学方程。基于祖冲之类方法的思想,结合辛龙格-库塔方法对微分-代数方程进行数值求解。数值算例说明本文建模方法和数值算法都是有效的,能很好地保持系统约束和能量。最后分析了绳长、平台系统的质量、轨道高度对于梁中点挠度和轴向平均应变的影响。     

Spectrum of Natural Vibrations of the Ice Ocean of Jupiter's Moon Europa

The hydroelastic vibrations of the ice surface of the ocean of Europa, a natural satellite of Jupiter, are investigated, and the natural spectrum of frequencies of this surface is determined. The mathematical model of the mechanical system under consideration is presented in the form of a spherical shell, which is wetted by a spherical layer of liquid enveloping a rigid spherical core. The solution of the boundary value problems of the theory of elasticity is sought in the form of expansions into series of the associated Legendre polynomials. It is noted that there are at least three tones of natural vibrations of the shell–spherical liquid layer system, whose periods lie in the vicinity of the ten-hour period of Jupiter's rotation about its axis, and variations of the magnetic field of Europa with the same period.     

A specific case of stability of cylindrical precession of a satellite

In a central Newtonian gravitational field, the motion of a dynamically symmetrical satellite along an elliptical orbit of arbitrary eccentricity is considered. The particular motion of the satellite is known when its axis of symmetry is perpendicular to the orbit plane, and the satellite rotates about this axis with a constant angular velocity (cylindrical precession). A nonlinear analysis of stability of this motion has been performed under the assumption that the geometry of the satellite mass corresponds to a thin plate. At small values of orbit eccentricity e the analysis is analytical, while numerical analysis is used for arbitrary values of e.     

用模态参数和振动试验数据修正动力学环境模型的研究

文章提出了一种利用模态参数和由振动试验数据求得的频响函数来进行模型修正的方法.在已建立的初步动力学模型的基础上,首先用实测的模态参数对解析模型进行修正,然后再用实测的频响函数修正解析模型的动力学参数,以使修正后的动力学模型中的模态参数和加速度频响函数与实际测量值一致.文章给出了这种方法的数学原理和公式,并通过一个数值模拟实例分析并验证了修正后模型的精确性.     

A Modification of the Method of Transporting Trajectory

Further development of an approximate method for optimizing a flight with an ideally controlled small thrust is proposed. The method is based on the employment of the transporting trajectory and considered in [1–3]. A detailed analysis of the means of improving the accuracy of this method suggested in [2, 3] is carried out, and the solution is presented in finite form. The proposed approach is applied to the flights making flybys of many celestial bodies. In the case of small bodies the solution is also obtained in finite form. A numerical example is considered confirming the high efficiency of this method.     

Numerical Simulation of Impact Loading on Solid Propellant Within an Orthotropic Shell

The strain–stress state of the solid propellant rocket engines (SPREs) is simulated under impact. The effect of orientation of elastic and strength properties of orthotropic organoplastic shell material on the strain–stress state of the solid propellant is investigated. Normal and oblique impact of single steel cylinder projectiles, both simultaneous and at different times of multiple, converging steel spheric particles with SPRE are investigated in this study. The investigation is conducted numerically. The numerical modeling was carried out in a three-dimensional formulation by the method of finite elements for the continuous approach of the mechanics of a deformable solid. The destruction of the anisotropic material is described by the tensor-polynomial criterion of the fourth degree, which takes into account the influence of hydrostatic pressure.     

低重力环境下三维液体非线性晃动的数值模拟

本文讨论低重力环境下三维液体非线性晃动问题。采用ＡＬＥ（任意的拉格朗日－欧拉）运动学描述跟踪自由液面；对于ＡＬＥ描述的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，在时间域上采用分步离散方法中的速度修正格式进行数值离散，在空间域上利用有限元方法进行了数值离散；推导了考虑表面引力效应时有限元边界条件的弱积分形式；给出了表面张力的数值计算公式。模拟了考虑表面张力情况下圆筒型贮腔中液体的非线性晃动，并得到了贮腔壁面处     

A fast numerical approach for Whipple shield ballistic limit analysis

Whipple shield is widely used on manned spacecraft, numerical simulation is an important way for obtaining the ballistic limit. The large population of particles and the large space span of Whipple shield simulation model restrict the computational efficiency. A fast numerical approach is presented for Whipple shield ballistic limit analysis. First, the critical penetration analysis of the rear walls is converted into specific impulse analysis delivered by the secondary debris cloud, because the maximum of specific impulse is the main determinant of the penetration. The dual plate simulation model is then converted into single plate model and the population of particles is reduced. Second, based on the isotropic expansion theory of secondary debris cloud, the specific impulse analysis is further converted into particle position and velocity analysis when the stable secondary debris formed. The space span of the simulation model is reduced. An example of Whipple shield ballistic limit analysis is provided for the verification of the fast numerical approach, it shows that this approach can significantly increase the computation efficiency with acceptable accuracy.     

增强飞行器角闪烁的方法—一种新的飞行器隐身技术

本文建立了任意截面缝隙加载理想导体柱电磁散射的一般数学模型，获得对缩比模型的理论计算与测量数据较好的一致性。在谐振频率区内对实际模型测量分析表明，利用多背接腔缝隙加载，可以实现较大姿态角范围内后向雷达散射戴面的减缩，并同时产生目标角闪烁线偏差有强烈增强，这是一种新的飞行器隐身技术措施。