deletions | additions       diff --git a/If_we_assume_vec_v__.tex b/If_we_assume_vec_v__.tex  index 3300d14..2ec1a35 100644  --- a/If_we_assume_vec_v__.tex  +++ b/If_we_assume_vec_v__.tex 
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If we assume  $$ 2  \vec{v}(t) \Delta t = \vec{x}(t+\Delta t) - \vec{x}(t-\Delta t) $$ then  $$\vec x(t+\Delta t) - \vec{x}(t-\Delta t) = 2\vec x(t)-2 \vec x(t-\Delta t)+\vec a(t)\,\Delta t^2$$  $$\vec{v}(t) $$2 \vec{v}(t)  \Delta t = 2\vec x(t)-2 \vec x(t-\Delta t)+\vec a(t)\,\Delta t^2$$ $$\vec{v}(t) \Delta t = \vec x(t)- \vec x(t-\Delta t)+\frac{1}{2}\vec a(t)\,\Delta t^2$$  which is \textit{exactly} Velocity Verlet for $\vec{x}$.