RELATIONSHIPS FOR MOTION DESCRIBED IN ANY TWO ROTATIONAL REFERENCE FRAMES

In this paper the definitions of the relative derivatives of a vector with respect to time in any reference frame by using the notation of vectrix are proposed. It is further shown that with the help of vectrix one can treat the relative derivatives more clearly and more rigorously when multiple reference frames are concerned. Very useful relationships between the first order relative derivatives described in any two reference frames are derived. Relationships for the second order relative derivatives are also presented in detail. A new concept called "rotation induced acceleration" which is caused by the rotation of two reference frames when motion is necessarily described in them is presented. The result obtained in this paper is the generalization of the acceleration theorem given in conventional theoretical mechanics.     

Structure and kinetic properties of slow-mode shocks associated with magnetic reconnection in the near-Earth magnetotail

We study the structure and kinetic properties of slow-mode shocks near the plasma sheet boundary layer (PSBL) associated with magnetic reconnection by Cluster observation. The presence of slow-mode shocks is confirmed by traditional Rankine–Hugoniot (RH) analysis and Monte-Carlo shock fitting method. The Walén analysis, applied to the tailward flow associated with slow-mode shocks, also supports that plasma was accelerated across a Petschek-type slow-mode shock connected to the diffusion region. Back-streaming ions were observed on the shock layer, and cold ions were accelerated and heated by slow-mode shocks. In addition, whistler and electrostatic solitary waves were observed around the slow-mode shocks. These waves might be excited by the observed field-aligned electron beams near the shocks.     

计算大型实对称特征问题的 Lanczos-QR 算法

为了计算大型实对称特征值问题Ｋｘ＝λＭｘ的少数低阶特征值对，本文给出Ｌａｎｃｚｏｓ－ＱＲ迭代方法。首先，给定初始迭代向量ｖ１，作ｍ步Ｌａｎｃｚｏｓ分解：ＫＶｍ＝ＭＶｍＴｍ＋ｈｍｅｍＴ。取Ｔｍ的ｄ个最大特征值为移位量，对Ｔｍ进行ｄ步带原点位移的ＱＲ分解。然后，修改初始迭代向量ｖ１。迭代地重新开始这一过程，迫使初始迭代向量ｖ１进入需求的特征子空间，从而使残量‖Ｋｘ－θＭｘ‖→０。数值例子表明，该方法收敛性强，且稳定、有效。     

可压缩流动激波装配在格心型有限体积法中的应用

发展了一种基于格心型有限体积方法(FVM)的激波装配算法。通过定义网格节点属性可以灵活调用激波装配和激波捕捉计算方法。在使用激波装配方法时,激波节点运动速度和下游运动速度通过Rankine-Hugoniot(R-H)关系式获得,同时采用非结构动网格技术描述激波的运动以及调整其他网格节点的位置。流过激波面元的通量为上游单元的基本通量,物理概念更加清晰,通量计算也更为准确。在计算过程中,网格节点属性可以发生变化,以此实现对带有拓扑变化流场的描述。数值试验表明:本文提出的计算方法不但具有较高的计算精度,同时能有效地避免由于捕捉激波而出现的数值问题。     

拖靶系统挂机安装角度计算

拖靶安全释放是拖靶系统正常执行任务的前提,拖靶挂机安装角度的优劣直接影响着拖靶的安全释放.依据拖靶释放特性建立了拖靶系统动力学模型,提出了拖靶安全释放的条件,给出了拖靶挂机安装角度的计算方法;通过实例对方法的正确性进行了验证,其结果直接应用于某新型拖机改装试验中,取得了满意的效果.     

大型水陆两栖飞机侧风起降的滑流影响分析

大型水陆两栖飞机AG600的动力装置为安装在机翼上的4台同向旋转涡轮螺旋桨发动机，针对1：15缩比模型带动力风洞试验显示的螺旋桨滑流对侧风起降状态的偏航力矩不稳定影响，对全机带动力风洞试验模型进行了大规模并行非定常数值计算，再现了风洞试验现象，通过流动机理分析明确其产生原因主要是左侧滑时右外翼分离和垂尾背鳍涡破裂，这些原因和数值模拟的准确性也为后期的风洞试验所证实。考虑到模型风洞试验中尺度限制造成的低雷诺数和高螺旋桨转速，为保证飞行安全，继续采用该非定常方法对全尺寸飞机真实侧风起降状态进行了详细数值分析和偏航稳定性评估。研究结果显示，在飞行雷诺数和螺旋桨转速下，相同侧风范围内风洞试验显示的流动不稳定因素基本消失，偏航稳定性允许的侧风范围明显增加。本研究实现了四发螺旋桨飞机起降状态横向气动特性的滑流影响非定常数值分析，建立了基于计算流体力学的风洞与飞行雷诺数效应的相互关系，进行了偏航稳定性的虚拟试飞评估，研究成果也为AG600飞机的首飞和飞行试验所验证。     

二维三角晶格的Peierls相变前后的声子色散曲面的研究

利用晶格动力学理论计算了二维三角晶格的Peierls相变前后的声子能谱。并且在第一布里渊区绘制了声子色散曲面。通过对Peierls相变前后的声子能谱比较可知，随其对称性降低，声子能谱的简并度被破缺。二维三角晶格的Peierls相变前只有两支声频支声子能谱，Peierls相变后有两支声频支声子能谱与两支光频支声子能谱，并且声频支声子能谱与光频支声子能谱不相交，两支光频支声子沿ky轴平缓地变化。     

轮控小行星探测器建模及跳跃移动仿真

小行星探测器在弱引力环境下无法采用传统的轮式机构进行移动。为解决该问题,采用反作用飞轮对探测器跳跃移动进行控制,并分析了该方案的可行性。根据Hertz碰撞定律及简化的Karnopp切向摩擦力模型,建立了探测器与地面的接触力模型。分析了轮控小行星探测器的起跳过程,给出了探测器静止起跳所需要的最小飞轮力矩关系。考虑到反作用飞轮存在惯性、粘滞、摩擦等情况,建立了轮控探测器的姿态动力学模型,并对探测器在均匀重力场下的连续跳跃过程进行了控制策略设计及仿真。结果表明:基于飞轮控制的小行星探测器跳跃移动在微重力环境下是可行的,且可以通过施加合适的控制力矩维持探测器跳跃的方向及跳跃过程的稳定性。     

激光功率与底面状态对选区激光熔化球化的影响

为研究激光功率与底面状态对选区激光熔化熔池流动的影响，基于离散单元法建立了选区激光熔化铺粉模型，采用粒径分布与实验相符的马氏体时效钢粉末分别铺展到平坦底面和增材底面上，将计算获得的粉末分布导入到基于有限体积法建立的选区激光熔化熔池计算流体力学模型中，研究激光功率和基板底面粗糙度对熔池流动和熔道表面形貌的影响。采用激光单道扫描实验验证铺粉模型和选区激光熔化模型。结果表明：随着激光功率的降低，单位长度的球化数量增加；由于增材底面使熔池润湿性变差，同时又对熔池流动行为产生扰动，使得增材粗糙底面上熔道的球化数量增加。选区激光熔化铺粉模拟及激光单道扫描模拟结果与实验结果吻合较好。本研究可为选区激光熔化工艺中工艺参数的选择提供理论指导。     

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune–Triton system

The problem of a spacecraft orbiting the Neptune–Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune’s satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a × I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton’s orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L₂, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincaré section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method.