全微分求偏导法和比较系数方法的同一性

给出了全微分求偏导法的证明,指出了比较系数法和全微分求偏导方法的同一性,并且给出了具体的例子.

微振动力学系统模型构造微分方程系数矩阵方法

对于多自由度定常约束微振力学系统的数学建模有许多方法 ,但这些方法不是受到使用条件限制就是计算繁琐 ,并且不适合于计算机建模。根据系统的动能、势能、耗散能量与运动方程决定的动能、势能、耗散能量分别相等的原理 ,提出了构造微分方程系数矩阵方法 (下称能量偏导法 )。论证了直接法[1] 、视察法[2 ,7] 是能量偏导法的特例。能量偏导法的优点是 :在建立运动方程的过程中 ,设有对时间求导的过程 ,也没有对方程整理和化简的过程。该方法既适用于单自由度系数又适合于多自由度系统 ,既适用于手工建模又方便于计算机建模。在该方法的基础上 ,本文又提出了运动方程解耦的数学条件 ,为广义坐标的选取指明了方向。文中也给出了能量偏导法的应用和结论。

电镀产品的公差与二元变闭曲线

从常数到变量的飞跃,从定曲面到变曲面的探索,前景乐观.本文由电镀并简化为二维情形引出含双参量的变化闭曲线.通过建立法微分等概念,使变闭曲线的变化性状可用多元微分加以处理,建立了电镀公差估计及优化参数的微分基础,并导出有关性质.

Construction of Wave-free Potentials and Multipoles in a Two-layer Fluid Having Free-surface Boundary Condition with Higher-order Derivatives

There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.

Design and simulation for large parafoil fix line object homing algorithm

Traditional parafoil homing usually uses a point as object. As the mobility of parafoil is limited by its glide ratio and wind, in some cases when the parafoil scatter area is large, or the glide ratio of parafoil is small, the deviation of its landing point to object point will be arduous to control. Accordingly, during these situations, when parafoil is used in recovery of spacecraft or satellite, the landing area of parafoil can be set as a rectangle, and the object of parafoil can be set as a line segment. The thesis of this work is designing an algorithm for parafoil homing using line segment as object. The algorithm of wind velocity and direction calculation in different flying segments was also investigated. The algorithm designed navigates the parafoil to land into the predestined area and largely reduce the probability of recovery loads falling to unwanted area to damage houses and people.

从不同视角看高中数学“线性回归分析”的两个结论

【目的】探索普通高中课程标准实验教科书数学学科中所反映的初、高等数学之间的关联性。【方法】以《回归分析的基本思想及其初步应用》中的两个结论为例,从不同视角进行分析、推导及证明。【结果】探索了这些方法之间所展现出的关联性,加深了对数学知识的融会贯通。【结论】普通高中数学课程是衔接初等数学与高等数学的纽带,从不同角度对其进行认知,有利于加深对相关数学概念的理解和掌握。