复连通区域曲线积分与路径无关的充要条件

本文主要给出了复连通区域曲线积分与路径无关的充要条件,同时进一步讨论了当曲线积分与路径相关时,沿不同路径的积分之间的某种关系。     

关于曲线积分教学的几点思考

本文主要阐述对曲线积分教学的几点思考,即数学思想方法在教学中渗透,教育数学在教学中应用,激发探讨数学概念的兴趣,利用几何直观揭示两类曲线积分概念间的关系,加深学生对曲线积分的理解。     

一种利用动态模量主曲线估算抗拉强度主曲线的方法

为获得抗拉强度主曲线,基于动态储能模量主曲线、应力松弛模量主曲线和Griffith方程,建立了固体推进剂动态和静态单向拉伸力学性能之间量化关系,即考虑温度折算后,推进剂抗拉强度之比等于动态模量相应变换后的均方根之比。依据这种关系,可从动态模量主曲线估算出推进剂在任意温度和拉速下的应力值,进而绘制成抗拉强度主曲线。将计算值与实测值进行对比,结果较一致。利用所得抗拉强度主曲线,可推广用于评估推进剂药柱是否具备承受点火冲击的力学性能。     

曲线合成孔径雷达最佳孔径研究

基于曲线合成孔径雷达原理与空间几何关系，讨论了曲线合成孔径雷达信号模型与成像方法，推导出目标的一维信号模型、二维信号模型，并将其扩展到了三维信号模型。考虑到不同的曲线孔径形状将对方位分辨率和高度分辨率有不同影响，详细研究了各种不同形状的曲线孔径，分析和对比了各种形状的孔径，给出了各自的优缺点和适用条件。结论是上下、左右对称的孔径形状较不对称的效果更优，L型孔径将导致很高的旁瓣。仿真实验可以对真实飞行航迹起指导作用。     

基于活动标架对Gosper曲线的研究

基于活动标架定义离散曲率^[1-3],并借此研究了Peano-Gosper分形曲线,得出一种新的生成Peano-Gosper空间填充曲线算法。通过建立曲线弯曲点位置号码与弯曲点曲率的映射,对于任意正整数n,能够输出对应弯曲点的曲率并画出相应弯曲点图象结构。相比于传统生成Peano-Gosper分形曲线的方法,本文算法减少迭代次数提高效率。     

HTPB推进剂裂纹起裂J积分研究

为研究HTPB推进剂的裂纹起裂特性,建立了一种由单试件计算推进剂J积分和JV积分的方法,开展了HTPB推进剂松弛试验和含I型裂纹平板试件J积分试验,标定了试件的裂纹构型因子,得到了推进剂的载荷-虚位移曲线以及裂纹起裂J积分和JV积分值。结果表明,文中建立的方法能够很好地计算推进剂的裂纹起裂J积分和JV积分值,推进剂的J积分和JV积分具有明显的率相关性,随着加载速率的增加,其值也变大,且加载速率对JV积分的影响比对J积分的影响要大得多。     

回流焊温度曲线热容研究

本文全面的分析了回流焊温度曲线在回流焊工艺中的作用,回流焊工艺的工艺特点、影响回流焊温度曲线的各种因素.如何从热容的思想建立回流焊温度曲线的方法?如何调整温度曲线通过控制温度曲线改善工艺过程,减少回流焊工艺的缺陷?     

图像加密方法研究

本文提出了一种图像加密方法。把扰乱像素地址法与椭圆曲线密码体制相结合，既保留了椭圆曲线密码体制的优越性，又具有加密速度快的特点。     

回流焊温度曲线热容研究

本文全面的分析了回流焊温度曲线在回流焊工艺中的作用，回流焊工艺的工艺特点、影响回流焊温度曲线的各种因素。如何从热容的思想建立回流焊温度曲线的方法？如何调整温度曲线通过控制温度曲线改善工艺过程，减少回流焊工艺的缺陷？     

航天器环绕小行星Ivar的运动分析

将小行星Ivar近似为三轴椭球体，给出了非球形引力势函数，建立了航天器环绕小行星Ivar的轨道动力学方程。利用Jacobi积分常数绘制了航天器在Ivar周围的零速度曲线，并分析了航天器的可能运动区域，给出了航天器不碰撞小行星Ivar的边界条件及不同偏心率下的近拱点半径。分析了小行星Ivar扁率和椭率对环绕轨道的影响，数学仿真结果表明：在一个轨道周期内，顺行轨道的开普勒能量、轨道角动量、偏心率和近拱点半径变化较大，而逆行轨道的相应参数变化较小。     

Between a celestial body and a spacecraft: Making the space elevator a success

The space elevator will operate in near-Earth space, under the attraction of the Earth, the Moon and the Sun. It will have to avoid collisions with active satellites, with space debris and with meteoroids, not counting other minor adverse phenomena. The exceedingly long cable cannot be a passive and limp body. It must be an active part of the elevator, withstanding lunisolar and other perturbations threatening its stability. The cable must have sensors and thrusters at appropriate locations along the cable. Sensors would serve for detection of objects on a collision course and thrusters for station-keeping and for initiating evasive manoeuvres. Adaptive control must be used for that purpose. Extensive series of numerical simulations will have to be performed to ascertain that the elevator is stable and that possible oscillations do not interfere with the main function of the elevator.     

Motion of a Planet with a Complex Structure

The motion of a planet consisting of a mantle and a core (solid bodies) connected by a viscoelastic layer and interacting with each other and an external point mass by the law of gravitation is considered. The mutual motions of the core and mantle are investigated assuming that the centers of mass of the planet and external point mass moves along undisturbed Keplerian orbits around the common center of mass of the system. The planetary core and mantle have an axial symmetry and different principal moments of inertia, which leads to a displacement of the center of mantle relative to the center of core and to their mutual rotations. The results obtained on the basis of averaged equations are illustrated by the example of the Earth–Moon system.     

Equilibrium positions of a weight on a cable fixed to a dumbbell-shaped space station moving along a circular geocentric orbit

The motion of a space object in the gravitational field of the Earth is considered. The object consists of an extended space station and a weight, which is free to move along the cable fixed to the ends of the station. It is assumed that the station is composed of two masses coupled by a weightless rod, while the cable is weightless and non-stretched. The equations of motion of such a system are derived for the case when the motion proceeds in a single plane, while the center of mass of the system moves along a circular geocentric orbit. The conditions of the cable tension (conditions of being on tie) are derived. The phase portrait of the weight motion along the cable is constructed when the station is oriented to the attracting center or is perpendicular to this position. The possibility to leave the tie in this case is analyzed. Equilibrium configurations of the system are found, i.e., such motions of the object under consideration at which the weight does not change its position relative to the station. Lyapunov stability of such configurations is analyzed for two situations: when the station is composed of equal masses and when masses at the ends of the station are different. In particular, for the case of different masses it is established that there exist such positions of equilibrium at which the dumbbell is located at an angle to the direction to the attracting center. In some cases these positions can be stabilized (if the weight is fixed on the cable).     

拆掉阻挡思维的墙——从航天员教员到模拟航天员的跨界选择

当凭借影片《国王的演讲》获得第83届奥斯卡金像奖最佳男主角的科林·弗斯（ColinFirth）,在国际顶级生物学学术期刊《Cell》的子期刊《CurrentBiology》上发表了一篇极为专业的科研论文时,全世界一片哗然,为之震惊!当电影《泰坦尼克号》导演、年届57岁的卡梅隆驾驶单人深潜器下潜至马里亚纳海沟海渊底部的时候,我们看到了一个雄心勃勃的跨界玩家。为什么时下如此多的人开始拆掉阻挡思维的墙？因为界外的世界很精彩!     

Navigation Solution to Maneuver a Spacecraft Relative to a Sphere Centered on a Cooperative Satellite

A differential correction algorithm is presented to deliver an impulsive maneuver to a satellite to place it within a sphere, with a user defined radius, centered around a non-maneuvering satellite within a constrained time. The differential correction algorithm develops and utilizes the State Transition Matrix along with the Equations of Motion and multiple satellite?s state information to determine the optimum trajectory to achieve the desired results. The results from the differential correction algorithm are very accurate for prograde orbits, as presented. The results allow for orbit design trade-offs, including satellites? initial inclinations, semi-major axes, as well as the ballistic coefficients. The results also provide an empirical method to determine the optimum ΔV$\mathrm{\Delta }V$ solution for the provided problem. Understanding that the minimum fuel solution lies with a semi-major axis ratio of 1, a very accurate empirical approximation is presented for semi-major axis ratio values less than and greater than 1. This work ultimately provides the generalized framework for applying the algorithm to a unique user defined maneuvering spacecraft scenario.     

Force on a coil moving above a grid structure

The force on a coil moving with a high-speed parallel to a conducting grid consisting of parallel tubes is investigated. The coil performs a rebound motion or an oscillatory heave motion when pressed toward the grid by reactive on-board engines. The coil is approximated by two parallel wires moving parallel to the grid tubes. The corresponding electrodynamic problem is two dimensional and is solved by expansions in terms of Bessel functions. Expressions are derived for the lift and drag force as well as the heat generated in the tubes in the limit of strong skin effect. The dependence on the grid spacing is analysed in the approximation of no mutual inductance between the tubes. Two specific applications are a shunt deflecting the coil, and a funnel leading to multiple reflection. Finally, the varying magnetic flux threading the coil is considered and the thermal load of the coil is estimated.     

On a distorted flame front as a hydrodynamic discontinuity

The radius of curvature of a steady distorted flame often turns out to be considerably larger than the width of the thermal structure of the flame. Thus, even under finite deformations of the flame, its structure remains quasi-one-dimensional. This property enables the propagation velocity of a distorted flame front (relative to the gas) to be determined explicitly as a function of the hydrodynamic field and the physico-chemical parameters of the gaseous mixture. With the aid of this relationship one can try to determine the shape of the front in a model which is external with respect to the flame structure and treats the flame as a density jump in an ideal incompressible fluid. As applications, we consider (1) the structure of a Bunsen cone, (2) the extinction of a flame in a divergent flow and (3) the propagation velocity of a corrugated flame.     

Optimal Control of a Programmed Turn of a Spacecraft

A problem of optimal turn of a spacecraft is considered. The time of turn is minimized, as well as the functional having a meaning of the propellant consumption. An analytical solution to the problem stated is derived. It is demonstrated that the solution optimal in this sense belongs to a class of two-impulse controls, under which a spacecraft executes the turn along the trajectory of its free motion. The solution obtained in this paper differs from earlier available solutions considerably. The estimations of the propellant consumption for a realization of the programmed turn are made.     

Peristaltic transport of a viscoelastic fluid in a channel

This paper is devoted to the study of the peristaltic transport of viscoelastic non-Newtonian fluids with fractional Maxwell model in a channel. Approximate analytical solutions have been constructed using Adomian decomposition method under the assumption of long wave boundary layer type approximation and low Reynolds number. The effects of relaxation time, fractional parameters and amplitude on the pressure difference and friction force along one wavelength are received and analyzed. The study is limited to one way coupling model with forward effect of the fluid on the peristaltic wall. It is evident from the result that pressure diminishes with increase in relaxation time and the effects of both fractional parameters on pressure are opposite to each other. The influences of these parameters on friction force are opposite to that of pressure.