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球坐标下的 三重积分计算

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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  1. 球坐标下的三重积分计算

  2. 球面坐标 z 0 y x z M(r,,) . . . r  y  x N

  3. 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

  4. . 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 

  5. 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

  6. . 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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