二阶中立型方程周期解的存在性

利用Ｆｏｕｒｉｅｒ级数理论研究二阶常第数线性中立型方程的周期解，得到了在｜ｃ｜＝１的条件下，二阶中立型方程周期解存在的充要条件；在｜ｃ｜＝１条件下，方程周期解存在的充分条件，并给出了具有特殊时滞的方程周期解存在的充分条件。     

新的GPS单频单历元定姿算法

LAMBDA算法依赖于初始的模糊度浮点解,但仅用载波相位观测方程需要多个历元才能获得浮点解,将导致初始化时间过长.针对这一问题,对GPS(Global Positioning System)单历元的载波相位单差方程进行特殊变换,将未知的整周模糊度看成噪声,从而构造出新的观测方程,和原始的观测方程进行组合求解,克服了仅用载波相位双差观测方程因为亏秩而无法在单历元获得浮点解的缺点,解决了初始化时间的问题.通过深入研究浮点解和固定解之间的关系,提出一种将低精度浮点解映射到固定解的方法,降低了LAMBDA算法对高精度浮点解的依赖性,避免了用多个历元获取浮点解的高精度,从而实现了单频、单历元的整周模糊度估计.通过实际测试,该算法成功率高于97%,能够有效地用于实时动态姿态解算.      

Cahn-Hilliard-Schlgl反应-扩散方程分叉问题

本文利用Lyapunov-Schmidt约化方法、奇异性理论及摄动方法,对服从Cahn-Hilliard广义扩散定律的带有Schlgl反应项的Cahn-Hilliard-Schlgl反应-扩散方程的分叉情况进行了研究。研究结果表明,C-H-S方程可以产生单模态的空间周期一次和二次分叉。特别地,经小扰动的退化的C-H-S方程,在不同条件下,还可能产生不同形式的更为复杂的双模态混合的二次分叉。本文还给出了分叉类型和一次分叉解的近似表达式。     

冗余驱动直角坐标串并联机构动力学对比分析

对全新结构的万能直角串并联机构进行冗余驱动设计,通过建立动力学方程和欧拉方程,对机构的动平台各输入铰点处的受力状况进行了全面的分析,已知机构在给定空间位置和姿态下的输出端的受力、主轴的运动参数、连杆的运动参数、水平和垂直运动滑块的运动参数时,可以反向求解机构的动力学反解,通过计算机语言编程计算和绘图得到直观有效的结果数据,由此得知冗余驱动在改善原机构的动力学特性方面的良好表现.      

奇异摄动与鸭解

鸭解是近年来在奇异摄动方程的研究中发现并开始研究的，它是一种新的分支现象，关于这方面的结果不是很多，且在大多数文献中多采用非标准方法，本文则利和渐近分析法，微分方程定性理论及不动点方法，对一类特殊的单参数奇异摄动方程鸭解的存在性进行研究。给出了鸭解存在的充分条件及其所对应参数的估计；并给出了鸭解的近似表达式，利用这些结果可以清楚地描述这类方程当参数变化时相图的变化情况。     

空间6R串联机器人机构位置逆解新算法

将倍四元数的复指数形式应用于串联机构位置逆解分析中,提出了空间6R(R代表转动副)串联机构位置逆解新算法.基于倍四元数建立了空间6R串联机构位置逆解的数学模型;然后,使用线性消元和Dixon结式消元法,得到了6×6的结式;由于采用未知转角的复指数形式,不需要提取任何公因式,可直接获得该机构位置逆解的一元16次输入输出方程和全部16组封闭解.最后通过数字实例证明了该方法无增根无漏根.算例表明算法简洁,易于程序实现,为串联机构位置逆解分析提供了新的理论基础.     

飞行器姿态角解算的全角度双欧法

为了实现飞行器超机动飞行情况下姿态角的连续解算,将传统双欧法进行了改进.通过引入判别函数使得数值模拟过程中正反欧拉角能一一对应,克服了欧拉方程的奇异性,消除了传统双欧法须限定俯仰为 的限制,从而将正反欧拉角取值范围扩展到了全角度,实现了飞行器的任意姿态角连续解算.采用改进的双欧法数值模拟了飞机斤斗飞行动作,时间积分采用了变步长龙格库塔方法,结果表明该方法简单有效,能得到连续的高精度解.      

银河宇宙线的起源和初级质子谱

本文采用无界银河系的爆发点源各向同性弥散的模型研究了初级质子的输运方程.用加速器实验得到的P-P碰撞截面的最新资料和一个合理的扩散系数, 得到了该方程的解, 进而讨论了该解的一些特点以及诸多类似点源对地球附近质子谱的可能贡献.该模型所预期的质子谱能较好地说明实验结果.      

铁木辛柯梁固有振动频率的边界元解法

根据傅里叶变换推导具有两个广义位移的铁木辛柯梁固有振动的基本解.利用加权残量方法,从控制微分方程出发建立边界积分方程,进而根据边界条件得到频率方程,采用代数特征值方法和影响系数方法求解频率,并分析了两种方法的特点.以杆为例证明了对于一维均匀结构,对不同的边界条件利用边界元方法(BEM,Boundary Element Method)都可以得到精确频率.将铁木辛柯梁的BEM结果与有限元结果和精确解进行了比较.     

中心对称平面三连杆的同步运动

研究中心对称平面三连杆的运动.该模型是常见的力学系统,可以近似描述外层空间中弱引力条件下带有太阳能板的卫星的运动状况.然而,由于该系统是不可积系统,一般的运动状况比较复杂.在本文中对该模型建立Lagrange运动方程,主要研究其同步运动,求出同步运动的精确解,并分析其运动规律,证明了在一定条件下存在周期解.本文的结果为进一步研究该系统的在同步运动附近的复杂性打下了基础.      

Riccati方程的二次代数曲线解

Ｒｉｃｃａｔｉ方程一般没有初等解，但当它有初等解时，解很可能是代数曲线解。给出了Ｒｉｃｃａｔｉ方程存在二次代数曲线解的充要条件，及其有效的求解方法。     

Bifurcation analysis of ion-acoustic waves for Schrödinger equation in nonextensive Solar wind plasma

Bifurcation analysis of ion-acoustic wave (IAWs) solutions of the nonlinear Schrödinger equation (NLSE) is explored for the first time in an electron-ion (e-i) magnetized solar wind plasma. The existence of ion-acoustic (IA) periodic, superperiodic, kink, antikink, compressive and rarefactive solitary wave solutions are revealed. Special values of Solar wind plasma parameters at a normalized distance from the Sun are considered for numerical simulation. The IA wave solutions are derived analytically. These solutions are analyzed numerically considering the influence of parameters, namely, wave number (k), velocity (V) of traveling wave and nonextensive parameter (q). Computational simulation reveals that only IA periodic wave grows in amplitude as waves moves from the Sun.     

基于实体单元的转子动力特性计算方法

现代航空发动机振动分析必须考虑各结构间的动力影响,因此,应该运用实体单元对发动机进行整机建模.为了在进行复杂转子系统动力特性分析时能够考虑陀螺力矩的影响,在对八节点六面体实体单元有限元动力方程推导的基础上,对通用有限元软件MSC/NASTRAN,利用DMAP语言进行二次开发,通过修改解题序列,加入陀螺力矩、科氏力和离心力的影响因素.在对典型结构计算分析的基础上,总结了转动结构振动的一些特点,通过对计算结果的对比,证明本程序在计算复杂旋转结构模型时能全面考虑壳体行波振动和转子进动的影响,指出了其在整机建模中的应用前景.      

Solitary,explosive and periodic solutions for electron acoustic solitary waves with non-thermal hot ions

A theoretical investigation has been made for electron acoustic waves propagating in a system of unmagnetized collisionless plasma consists of a cold electron fluid and ions with two different temperatures in which the hot ions obey the non-thermal distribution. The reductive perturbation method has been employed to derive the Korteweg–de Vries equation for small but finite amplitude electrostatic waves. It is found that the presence of the energetic population of non-thermal hot ions δ, initial normalized equilibrium density of low temperature ions μ and the ratio of temperatures of low temperature ions to high temperature ions β do not only significantly modify the basic properties of solitary structure, but also change the polarity of the solitary profiles. At the critical hot ions density, the KdV equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KdV equation. In the vicinity of the critical hot ions density, neither KdV nor modified KdV equation is appropriate for describing the electron acoustic waves. Therefore, a further modified KdV equation is derived. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the various KdV-type equations, is used here. Numerical studies have been reveals different solutions e.g., bell-shaped solitary pulses, singular solitary “blowup” solutions, Jacobi elliptic doubly periodic wave, Weierstrass elliptic doubly periodic type solutions, in addition to explosive pulses. The results of the present investigation may be applicable to some plasma environments, such as Earth’s magnetotail region.     

Solitary and periodic waves in magneto–rotating plasmas: Effect of the Kappa–Cairns distributed electrons

The nonlinear propagation of ion–acoustic (IA) waves in a magneto–rotating plasma is studied by considering the Kappa-Cairns electron distribution. Employing the perturbation scheme, Korteweg–de Vries equation is derived. It is seen that both positive and negative potential solitons can be supported in the present plasma model. The numerical results reveal that the Kappa-Cairns distributed electrons modify features of the electrostatic waves significantly. The effects of non–thermal parameters, plasma rotation frequency, ion temperature, and the wave propagation angle on electrostatic solitary wave structures are also discussed here. It is found that the plasma parameters considerably influence the propagation of IA waves in rotating plasmas. Furthermore, using the bifurcation theory of planar dynamical systems to the K-dV equation, we have presented the existence of solitary and periodic traveling waves. Our study may be helpful to understand the behavior of ion–acoustic wave in the rotating plasma.     

Effect of gravity field on the nonequilibrium/nonlinear chemical oscillation reactions.

Biological systems have evolved for a long time under the normal gravity. The Belousov-Zhabotinsky (BZ) reaction is a nonlinear chemical system far from the equilibrium that may be considered as a simplified chemical model of the biological systems so as to study the effect of gravity. The reaction solution is comprised of bromate in sulfuric acid as an oxidizing agent, 1,4-cyclohexanedione as an organic substrate, and ferroin as a metal catalyst. Chemical waves in the BZ reaction-diffusion system are visualized as blue and red patterns of ferriin and ferroin, respectively. After an improvement to the tubular reaction vessels in the experimental setup, the traveling velocity of chemical waves in aqueous solutions was measured in time series under normal gravity, microgravity, hyper-gravity, and normal gravity using the free-fall facility of JAMIC (Japan Microgravity Center), Hokkaido, Japan. Chemical patterns were collected as image data via CCD camera and analyzed by the software of NIH image after digitization. The estimated traveling velocity increased with increasing gravity as expected. It was clear experimentally that the traveling velocity of target patterns in reaction diffusion system was influenced by the effect of convection and correlated closely with the gravity field.     

有限β等离子体中密度和磁场不均匀驱动的动理学Alfven波

在分析有限β等离子体中的密度、磁场不均匀引起的漂移波不稳定性的基础上，剖析了漂移波不稳定性对动理学Alfven波激发的作用．动理学理论能正确地处理有限拉莫半径效应和波粒共振相互作用，本文根据带电粒子在电磁场中的运动特性，采用Vlasov方程描述离子运动，运用漂移动理学方程对电子运动进行描述．密度不均匀和磁场不均匀对产生漂移不稳定性的对比分析表明：在有限β等离子体中，密度不均匀比磁场不均匀更易激发漂移不稳定性，且密度不均匀激发漂移不稳定性中的能量转换和转移更为强烈．这种能量的转换为动理学Alfven波的激发提供了物理基础．所得数值解表明：动理学Alfven波在磁层中能广泛地被激发产生，特别是在磁层空间的极尖区、磁层顶和等离子体片边界层等具有明显的不均匀性区域中更容易被激发产生．本文的研究结果进一步表明动理学Alfven波对磁层空间中能量传输具有重要作用．     

基于卫星自旋的纯引力轨道万有引力干扰抑制

一个称为“内卫星”的验证质量块位于外卫星的内部空腔中,不与外卫星接触而自由飞行,由于外卫星的屏蔽,其不受大气阻力、太阳光压等干扰作用,沿着纯引力轨道飞行。外卫星会对内卫星产生万有引力作用,是内卫星纯引力轨道的主要残余干扰。根据卫星相对运动动力学方程,建立了万有引力干扰对内卫星纯引力轨道影响的分析模型;基于将外卫星绕轨道面法向旋转以调制万有引力的策略,建立了外卫星自旋对万有引力干扰影响的抑制模型。以内编队纯引力飞行系统为例,对比计算了外卫星有无自旋时万有引力干扰对内卫星纯引力轨道的影响。基于模型的分析表明,外卫星自旋能够显著抑制万有引力干扰对内卫星纯引力轨道的长期影响;实例计算表明,万有引力干扰的天长期影响能够降低5~7个数量级。     

扇面波导中TM模

根据波动方程和边界条件，利用分离变量法导出扇面波导中ＴＭ模场分量通用表达式，计算了具有不同的张角和内外单径比的扉面波导中ＴＭ模的截止波数，并列出数表，给出截止波长的精确和近似的表达式。     

Generation mechanisms of the ELF-ULF waves related to the flux transfer events

Satellite observations near the magnetopause and within the magnetosheath revealed the existence of some structures characterised by specific magnetic field and plasma signatures. They have been called “Flux Transfer Events”. One of the models of FTEs is a reconnected fluxtube, extending from the inner magnetosphere into the magnetosheath. ELF-ULF waves are often observed in together with other FTE's signatures. Wideband emissions are associated with the boundaries of FTEs with characteristic maxima at lower hybrid and ion-cyclotron frequencies. They provide a tool for better timing of the events. These emissions might also be related to the reconnection process. Observations of FTE's by Prognoz-8 satellite are presented in our paper. Wave signatures of the FTEs are described. Various mechanisms of generation of the emissions by instabilities depending on local plasma conditions are discussed along with non-local aspects of such waves. Numerical solutions of the dispersion equation for the typical conditions in FTEs are presented. Possible relation of these waves to the reconnection process are discussed.