Остроградский-Gauss公式的应用研讨

Probe into the Application of Остроградский-Gauss Formula

首先由Green公式引入O-G公式,然后利用O-G公式和第一型曲面积分与第二型曲面积分的关系,将空间区域的体积表为曲面的积分;再分别利用直角坐标与极坐标,解得了一般封闭曲面所围立体的体积;最后利用O-G公式计算曲面积分,得到了锥面与球面所围立体表面的外侧及一般封闭曲面所围立体表面的上侧。

First,O-G Formula is introduced by Green Formula,using O-G Formula and relation between the first and second types of curved surface integral,volume of spatial domain is expressed as curve surface integral.Then by the use of orthogonal coordinate and polar coordinate,volume of the solid enclosed by general closed suface is solved.Afterwards,curved surface integral is calculated through O-G Formula,last,the outboard and upside surface of the solid,enclosed by conical surface and spherical surface,and that enclosed by general curved surface are solved.