ベクトル微分演算子/回転公式 のバックアップの現在との差分(No.10) |
予備知識予備知識回転と元ベクトルの外積回転公式回転と元ベクトルの外積左辺
外積の回転外積の回転左辺左辺
回転の回転回転の回転&spandel; \:\nabla \vx (\:\nabla \vx \:F)&spanend; &spandel; = \:\nabla (\:\nabla \sx \:F) - (\:\nabla \sx \:\nabla) \:F&spanend; &spandel; = \:\nabla (\:\nabla \sx \:F) - \triangle \:F&spanend; &spanadd; \:\nabla (\:\nabla \vx \:F)&spanend; &spanadd; = \:\nabla \:F&spanend; &spanadd; = \:\nabla \:F&spanend;左辺左辺
内積の勾配#spanend &spanadd; \:\nabla (\:F \sx \:G)&spanend; &spanadd; = (\:G \sx \:\nabla)\:F&spanend; &spanadd; + (\:F \sx \:\nabla)\:G&spanend; &spanadd; + \:F \vx (\:\nabla \vx \:G)&spanend; &spanadd; + \:G \vx (\:\nabla \vx \:F)&spanend; #spanadd左辺 |