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Ghlen Livid added Let_us_derive_basic_Verlet__.tex
almost 8 years ago
Commit id: 1a1bbde17f6e827f285195f7b3d69649a9482c72
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Let us derive basic Verlet from velocity formulation:
$$\vec{v}(t) = \vec{v}(t - \Delta t) + \frac{\vec{a}(t - \Delta t) + \vec{a}(t)}{2} \Delta t$$
$$\vec{x}(t + \Delta t) = \vec{x}(t) + \vec{v}(t - \Delta t) \Delta t + \frac{\vec{a}(t - \Delta t) + \vec{a}(t)}{2} \Delta t^2 + \frac{1}{2} \vec{a}(t) \Delta t^2$$
$$\vec{x}(t) = \vec{x}(t - \Delta t) + \vec{v}(t - \Delta t) \Delta t + \frac{1}{2} \vec{a}(t - \Delta t) \Delta t^2$$
