>>337
v = da/dt とする
d|a|/dt = d√(a^2)/dt = ((1/2)/√(a^2)) da^2/dt
= (1/(2|a|)) da^2/dt = (1/(2|a|)) 2(a・v) = a・v/|a|

d/dt (a/|a|) = (da/dt/|a|) - (a/|a|^2)d|a|/dt
= (v/|a|) - (a/|a|^2)(a・v/|a|)
= (1/|a|^3)((a^2)v - (a・v)a)
= (1/|a|^3) a×(v×a)
= (1/|a|^3) a×0
= 0