【摘要】 本文根据回转体所应满足的基本边界条件,利用多项式的余数定理,导出了回转体横截面面积分布曲线的基本表达式。式中含有一个函数性参数。参函数的任一给定形式,可在“标准化坐标系”内生成一条回转体头部或尾部的型线;与此相反,任一给定型线上的各种信息,均可在参函数上得到反映,从而可以很容易地得出相应的数学表达式。文中给出的双参数系列,可以提供棱形系数范围很广的型线。 本文方法有着良好的逼近能力;采用本文方法,三参数的五阶多项式,一般情况下,即可得到良好的逼近效果。作为算例,文中给出了“Akron”飞船头部曲线的近似表达式。该表达式为一五阶多项式;但它能够给出比“Williams”的八阶多项式更为满意的近似结果。更多还原

【Abstract】 By means of the remainder theorem of polynomial, a so-called "basic mathematical expression" of the transverse cross sectional area curve of bodies of revolution is derived from the boundary conditions which have to be satisfied. Any given form of the parametric function in this expression will generate in the "normalized coordinate system" a figure of the fore or rear part of the bodies of revolution. On the contrary, the informations of a given figure can be taken into account and the parametric function will make the basic mathematical expression able to define it well.A two-parameter family of bodies of revolution given in this paper can be used to a wide range of prismatic coefficient.The given method is able to fit a given shape with good results, and, in general, a five-order polynomial is used for this purpose. As an example, the fore-body of the airship"Akron"is represented with the presented mathematical expression in the form of a five order polynomial, which is better than the William’s eight-order polynomial.更多还原