矢阵及其在目标状态测量建模中的应用

本文通过对引入矢阵反对称叉积算子概念，得出了矢阵叉积算子同一般矢量列阵叉积算子之间的关系恒等式，揭示了两者之间的对称关系，由此关系非常方便地得到了矢阵运动学关系及其它一些常用关系，并把坐标变换阵对时间的导数推广到一般的情况，一个对目标雷达被动定位状态测量建模的实例表明了其实际应用意义。     

工业计量中的基本问题述评

提出并讨论了工业计量中的几个基本问题；分析了其特点及解决方向；结合现状和可持续发展，讨论了工业计量的目的、体系、范围、问题等几个方面的内容及对策；提出了工业计量可持续发展的一种解决方案。     

正定几何规划及对偶问题的推导

给出了正定几何规划及对偶问题的有关定量证明，指出了原文献中凸数证明错误的地方，并补充了正确的证明。     

Resonant quasi-periodic near-rectilinear Halo orbits in the Elliptic-Circular Earth-Moon-Sun Problem

Motivated by the near-future re-exploration of the cislunar space, this paper investigates dynamical substitutes of the Earth-Moon’s resonant Near-Rectilinear Halo Orbits (NRHOs) under the Elliptic-Circular Restricted Four-Body Problem formulation of the Earth-Moon-Sun system. This model considers that the Earth and Moon move in elliptical orbits about each other and that a third body, the Sun, moves in a circular orbit about the Earth-Moon barycenter. By making use of this higher-fidelity dynamical model, we are able to incorporate the Sun’s influence and the Moon’s eccentricity, two of the most significant perturbations of the cislunar environment. As a result of these perturbations, resonant periodic NRHOs of the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) are hereby replaced by two-dimensional quasi-periodic tori that better represent the dynamical evolution of satellites near the vicinity of the Moon. We present the steps and algorithms needed to compute these dynamical structures in the Elliptic-Circular model and subsequently assess their utility for spacecraft missions. We focus on the planned orbit for the NASA-led Lunar Gateway mission, a 9:2 synodic resonant L₂ southern NRHO, as well as on the 4:1 synodic and 4:1 sidereal resonances, due to the proximity to the nominal orbit and their advantageous dynamical properties. We verify that the dynamical equivalents of these orbits preserve key dynamical attributes such as eclipse avoidance and near-linear stability. Furthermore, we find that the higher dimensionality of quasi-periodic solutions offers interesting alternatives to mission designers in terms of phasing maneuvers and low-altitude scientific observations.     

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.     

Construction of an airfoil with an irregularity in the flow

Using the method of quasisolutions for inverse boundary-value problems of aerohydrodynamics, a problem of constructing an airfoil was solved by the specified velocity distribution along the sought airfoil contour when there is an irregularity in the flow such as a vorticity source. The cases of a source (sink) and vortex are obtained as particular ones. The airfoils are constructed numerically and analytically and conclusions are made about an influence of the irregularity position and type on the shape and aerodynamic characteristics of the airfoil.     

广义均衡问题和不动点问题的收敛性定理及应用

运用平行算法，提出一种寻求广义均衡问题解及有限个严格伪压缩映像不动点集的公共元的新的迭代格式．在Hilbert空间中．证明了该算法的强收敛性。     

瞬态热应力问题的组合杂交有限元方法

求解瞬态热应力问题的杂交元方法面临Ladyshenskaya-Babuska-Brezzi(LBB)条件的检查,其稳定性难以保证,从而提出瞬态热应力问题的组合杂交有限元方法。建立瞬态热应力问题的基于区域分解的组合杂交变分原理及其有限元离散;通过数值算例验证求解瞬态热应力问题的组合杂交元的数值性能。结果表明:在大宽厚比网格下,八节点六面体组合杂交元(CHH(0-1))可以获得与二十节点六面体元(B20)精度相当的位移计算结果和更好的应力计算结果。     

四色定理论证的关键

一百多年来对"四色问题"的研究长期不得其解的关键在于:肯泊(A.Kempe)当年提出的"不可避免构形集"中一个国家(地域)具有五个邻国(邻域)的所谓"可约性"问题得不到解决。"《四色定理》论证"用数学归纳法,而"平面图的点着色方法"未用数学归纳法,两种方式论证"四色问题"都涉及到"一个(待着色)顶点有五个邻接顶点,已着有4种颜色,要将这4种颜色设法变成3种,把腾出来的1种颜色给该顶点着色。"———这就是四色定理论证的关键。再根据换色原理,用巧妙而深层次地换色办法,对这个关键进行更深刻地论述,其换(着)色最多六步就可以完成,进而更充实和完善了前述两文。     

用试验数据修正刚度矩阵

讨论用试验数据修正刚度矩阵的问题。依据特征方程、刚度矩阵的对称性和半正定性,利用代数特征值反问题的理论和方法,研究了这个问题解的存在性和唯一性,提出了修正刚度矩阵的一个新方法。用这个方法修正的刚度矩阵不仅满足特征方程,而且是唯一的对称半正定矩阵。