\:F \vx (\:\nabla \vx \:F) &spandel; = \ffd12 \:\nabla |\:F|^2 - (\:F \sx \:\nabla) \:F&spanend; &spanadd; = \ffd12 \:\nabla(\:F^2) - (\:F \sx \:\nabla) \:F&spanend; /home/limg/www/LimgMath/eq! Misplaced alignment tab character &. ...strut { \:F \vx (\:\nabla \vx \:F) & spandel; = \ffd 12 \:\nabl... l.34 $}
\:F \vx (\:\nabla \vx \:F) &spandel; = \ffd12 \:\nabla |\:F|^2 - (\:F \sx \:\nabla) \:F&spanend; &spanadd; = \ffd12 \:\nabla(\:F^2) - (\:F \sx \:\nabla) \:F&spanend;
/home/limg/www/LimgMath/eq! Misplaced alignment tab character &. ...strut { \:F \vx (\:\nabla \vx \:F) & spandel; = \ffd 12 \:\nabl... l.34 $}
左辺
外積の外積: ベクトル三重積:
積の微分のための式変形 *1 *2
右辺
積の微分: 積の微分:
ベクトル三重積: ベクトル三重積:
内積の交換則: 内積の交換則:
&spandel; \:\nabla \vx (\:\nabla \vx \:F)&spanend; &spandel; = \:\nabla (\:\nabla \sx \:F)&spanend; &spandel; - \:\nabla \sx \:\nabla \:F&spanend; &spandel; = \:\nabla (\:\nabla \sx \:F)&spanend; &spandel; - \triangle \:F&spanend; &spanadd; \:\nabla
/home/limg/www/LimgMath/eq! Misplaced alignment tab character &. $\displaystyle \mathstrut { & spandel; \:\nabla \vx (\:\nabla \vx ... l.34 $}
(\:\nabla \vx \:F)&spanend; &spanadd; = \:\nabla
/home/limg/www/LimgMath/eq! Misplaced alignment tab character &. ...yle \mathstrut { (\:\nabla \vx \:F)& spanend; &spanadd; = \:\na... l.34 $}
\:F&spanend; &spanadd; = \:\nabla
/home/limg/www/LimgMath/eq! Misplaced alignment tab character &. $\displaystyle \mathstrut { \:F& spanend; &spanadd; = \:\nabla } $ l.34 $}
\:F&spanend;
/home/limg/www/LimgMath/eq! Misplaced alignment tab character &. $\displaystyle \mathstrut { \:F& spanend; } $ l.34 $}
はと交換可能。 (がに依存しない限り)とは交換可能。
倍積の交換則: 倍積の交換則:
ラプラス演算子の猫式表記分数形: ラプラス演算子の凌宮表記の分数形:
#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
/home/limg/www/LimgMath/eq! You can't use `macro parameter character #' in math mode. $\displaystyle \mathstrut { ## spanend &spanadd; \:\nabla (\:F \sx... l.34 $}