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.1) |
予備知識外積の回転回転公式回転と元ベクトルの外積ナブラ表記:&spanadd; \:F \vx (\:\nabla \vx \:F)&spanend; &spanadd; = \ffd12 \:\nabla(\:F^2) - (\:F \sx \:\nabla) \:F&spanend; #spanadd左辺
外積の回転#spanend \:\nabla \vx (\:F \vx \:G) = (\:G \sx \:\nabla) \:F - (\:F \sx \:\nabla) \:G &spandel; - \:G (\:\nabla \sx \:F)&spanend; &spandel; + \:F (\:\nabla \sx \:G)&spanend; &spanadd; + (\:\nabla \sx \:G) \:F&spanend; &spanadd; - (\:\nabla \sx \:F) \:G&spanend;猫式導出:左辺
回転の回転#spanend &spanadd; \:\nabla (\:\nabla \vx \:F)&spanend; &spanadd; = \:\nabla \:F&spanend; &spanadd; = \:\nabla \:F&spanend; #spanadd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 |