In Verlet integration, why is $a*dt*dt$ considered "force vector"?
Intuitively, since Verlet integration is:
$$x_{i+1}=x_i+(x_i - x_{i-1}) + a * dt * dt$$
then this doesn't have other "force" terms than $a * dt *dt$. However I'm unsure as to what the $dt*dt$ does here.
It takes the centered difference approximation to the second derivative of $x$, namely $\frac{x_{i+1}-2x_i+x_{i-1}}{\Delta t^2}$, and sets it equal to $a(x_i)$ (implicitly assuming a force that is dependent only on position), and then solves for $x_{i+1}$.