deletions | additions       diff --git a/If_we_assume_vec_v__.tex b/If_we_assume_vec_v__.tex  index 4c437c5..3300d14 100644  --- a/If_we_assume_vec_v__.tex  +++ b/If_we_assume_vec_v__.tex 
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then  $$ \vec{x}(t+\Delta $$\vec x(t+\Delta t) - \vec{x}(t-\Delta  t) = \vec{x}(t) + \vec{v}(t) 2\vec x(t)-2 \vec x(t-\Delta t)+\vec a(t)\,\Delta t^2$$  $$\vec{v}(t)  \Delta t + \vec{a}(t)\Delta t^2 $$ = 2\vec x(t)-2 \vec x(t-\Delta t)+\vec a(t)\,\Delta t^2$$  which is \textit{exactly} Velocity Verlet for $\vec{x}$.