This is from text [Introduction to Lagrangian and Hamiltonian Mechanics] on NTNU opencourse. Annnnd... I don't use english as my primary language, so sorry for poor sentences. I can't get two things in here. First, at (1.12) I can't understand how L dot derivated like that. Since I know differentiation of cross product should be done like d/dt(AxB)=d/dt(A) x B + A x d/dt(B) then, at (1.12), why it doesn't have the terms of d/dt(r) x p ? I think it only has the terms of r x d/dt(p) Second, I can't get how were derived by using (1.13), How could ri X Fji = 1/2(rij X Fji) is possible? These might be dumb questions, but please help me.