Symmetry,reduction and relative equilibria of a rigid body in the J2 problem

The J₂ problem is an important problem in celestial mechanics, orbital dynamics and orbital design of spacecraft, as non-spherical mass distribution of the celestial body is taken into account. In this paper, the J₂ problem is generalized to the motion of a rigid body in a J₂ gravitational field. The relative equilibria are studied by using geometric mechanics. A Poisson reduction process is carried out by means of the symmetry. Non-canonical Hamiltonian structure and equations of motion of the reduced system are obtained. The basic geometrical properties of the relative equilibria are given through some analyses on the equilibrium conditions. Then we restrict to the zeroth and second-order approximations of the gravitational potential. Under these approximations, the existence and detailed properties of the relative equilibria are investigated. The orbit–rotation coupling of the rigid body is discussed. It is found that under the second-order approximation, there exists a classical type of relative equilibria except when the rigid body is near the surface of the central body and the central body is very elongated. Another non-classical type of relative equilibria can exist when the central body is elongated enough and has a low average density. The non-classical type of relative equilibria in our paper is distinct from the non-Lagrangian relative equilibria in the spherically-simplified Full Two Body Problem, which cannot exist under the second-order approximation. Our results also extend the previous results on the classical type of relative equilibria in the spherically-simplified Full Two Body Problem by taking into account the oblateness of the primary body. The results on relative equilibria are useful for studies on the motion of many natural satellites, whose motion are close to the relative equilibria.     

秦皇岛古代旅游诗歌整理及其对旅游的作用

秦皇岛作为历史悠久的旅游城市,拥有着大量的古代旅游诗歌,这些旅游诗歌对于传播秦皇岛的历史文化,推动旅游事业的发展起到了很大的作用。本文拟就秦皇岛古代的旅游诗歌整理分析及其在旅游中的作用三个方面展开论述。     

Non-Gaussian clutter characterization applied to OTHR using a mixture of two Rayleigh probability density functions

A practical technique for characterizing non-Gaussian radar clutter is specified and demonstrated using Over The Horizon Radar (OTHR) data, as an example. The technique employs maximum likelihood to fit the probability density of the clutter amplitude returns to a mixture of two Rayleigh probability densities instead of the single Rayleigh density typically used for Gaussian clutter. This model for non-Gaussian clutter is fully specified for any set of clutter amplitudes by a log likelihood, two Rayleigh parameters, and a mixing coefficient. A 3D plot of these values yields an easily-visualized clutter characterization, as is illustrated using OTHR data. This technique is a demonstration of clutter characterization using OTHR data, but the method can be applied to characterize other types of clutter data.     

非线性不确定系统的鲁棒镇定

讨论仿射非线性不确定系统的鲁棒镇定问题。给出了其鲁棒镇定的充分必要条件,以及一类非线性不确定系统,其鲁棒镇定界不依赖于其李雅普诺夫函数界的估计而仅依赖于其系统本身的结构性质与设计者的要求     

湍流模型对发动机排气系统流场和红外辐射特征计算的影响

计算分析了采用k-ω SST(shear-stress transport)模型、RNG(renormalization group)k-ε模型配合标准壁面函数(RNG k-ε+标准壁面函数)、RNG k-ε模型配合增强型壁面函数法(RNG k-ε+增强壁面函数)3种湍流模拟方法,对典型涡扇发动机轴对称收敛喷管排气系统流场、温度场、组分质量浓度场及红外辐射特征计算结果的影响.研究表明:对于这3种方法,排气系统腔体内壁面压力分布基本一致;但在温度场、组分质量浓度分布以及红外辐射特征方面的差别较大.RNG k-ε+增强壁面函数计算得到的内涵壁面与燃气流的温度、CO₂与H₂O的质量浓度和红外辐射强度值最大,RNG k-ε+标准壁面函数的计算结果其次,而k-ω SST 模型的计算结果最小.通过与试验结果对比,发现k-ω SST模型对排气系统红外辐射特征的模拟更加合理一些.      

关于哈密顿轨问题最小流模型的讨论

MasonIri论证了网络最小流问题可以在多项式时间内转换为哈密顿问题的模型与方法。本文利用一个反例指出了在该证明中使用的模型存在有不严格的地方。在此基础上,利用网络最小生成流的概念提出了一个修正模型,并证明了无环最小生成流问题可以在多项式时间内转换为哈密顿圈问题。文中最后指出,这一新的模型为解决在有向图内构造哈密顿轨的有效算法提供了一个新的思路和方法     

滚动轴承疲劳强度分布计算

根据P－S－N曲线上疲劳寿命存活率和疲劳强度存活率的等同性原理，借助已知的给定载荷下疲劳寿命概率密度函数，计算出未知的给定寿命下疲劳强度概率密度函数，进一步进行可靠性分析奠定基础。     

旋转圆盘振动的动态有限元法

本文将动态有限元法推广应用于轴对称圆板在旋转状态的振动特性分析,推导出环板元的动态形函数,解决了含贝塞尔函数的疑难积分问题,并建立了单元质量和刚度矩阵以及附加刚度矩阵和一次修正矩阵。文中以算例考核,结果与精确值比较符合。最后作为具体应用实例,分析了圆盘的固有频率随转速的变化情况。     

任意截面支臂加载波导T形结的矩量法分析

本文采用矩量法分析了任意截面支臂加载矩形波导T形结。首先根据等效原理将所研究的波导T形结分成两个独立的区域,把这两个区域中的磁场用支臂端口面上的等效磁流源和并矢格林函数的积分形式来表示,根据端口面上磁场切向分量的连续性条件建立了关于等效磁流源的积分方程。然后运用矩量法将该积分方程转化为矩阵方程,求解矩阵方程可得支臂端口面上等效磁流源的近似解。最后由等效磁流源导出了矩形波导T形结的散射参数。文中对两种不同结构的波导T形结在主模激励下的散射特性进行了数值计算,结果与现有文献中给出的数据吻合一致,从而证明了本文方法的有效性。     

射流和圆柱尾流湍流层次结构的实验研究

用热线测量了射流和圆柱尾流湍流核心区不同位置处的风速脉动 ,通过对速度结构函数标度性质的计算 ,研究了湍流层次结构模型。主要结论有 :层次结构模型中的相似性假设得到了实验的有力支持 ;模型提出的标度指数公式精确地反映了湍流随机场的标度性质 ;速度结构函数的标度性质是与具体湍流流动有关的。