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球坐标下的 三重积分计算 PowerPoint PPT Presentation


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球坐标下的 三重积分计算. 球面坐标. z. 0. y. x. z. M ( r ,  ,  ). r. . y. . x. N. 球面坐标的坐标面. z. 0. x. y. 动点 M ( r, ,  ). r = 常数 :. 球面 S.  = 常数 :. M. . r. S. z. 0. x. y. 球面坐标的坐标面. C. 动点 M ( r, ,  ). r = 常数 :. 球面 S.  = 常数 :. 锥面 C. M.  = 常数 :. 半 平面 P. . . S.

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球坐标下的 三重积分计算

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6417909

球坐标下的三重积分计算


6417909

球面坐标

z

0

y

x

z

M(r,,)

.

.

.

r

y

x

N


6417909

球面坐标的坐标面

z

0

x

y

动点M(r,,)

r =常数:

球面S

=常数:

M

r

S


6417909

.

z

0

x

y

球面坐标的坐标面

C

动点M(r,,)

r =常数:

球面S

=常数:

锥面C

M

=常数:

半平面P

S

P


6417909

球面坐标下的体积元素

z

0

y

x

元素区域由六个坐标面围成:

球面r+d r

圆锥面

半平面 及+d ;

半径为r及r+dr的球面;

圆锥面及+d .

dr

rsin

rsind

球面r

rd

圆锥面+d

r

d

d


6417909

.

球面坐标下的体积元素

z

元素区域由六个坐标面围成:

半平面 及+d ;

半径为r及r+dr的球面;

圆锥面及+d .

dr

rsind

dV

rd

dV =

r 2

sin drdd

r

d

0

y

d

rcos )

r 2

sin drdd

x


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