this is for holding javascript data
Ghlen Livid added widetilde_vec_v_t_Delta__.tex
almost 8 years ago
Commit id: 17ed47e701ab689d6d2f8af6271db353262c61af
deletions | additions
diff --git a/widetilde_vec_v_t_Delta__.tex b/widetilde_vec_v_t_Delta__.tex
new file mode 100644
index 0000000..9ef2142
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+++ b/widetilde_vec_v_t_Delta__.tex
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$$ \widetilde{\vec{v}}(t) \Delta t = \vec{x}(t) - \vec{x}(t-\Delta t) + \frac{1}{2} (\vec{x}(t+\Delta t) - 2\vec x(t) + \vec x(t-\Delta t)) $$
$$ \widetilde{\vec{v}}(t) \Delta t = \vec{x}(t) - \vec{x}(t-\Delta t) + \frac{1}{2} \vec{a}(t) \Delta t^2 $$
$$\vec x(t+\Delta t)=2\vec x(t)-\vec x(t-\Delta t)+\vec a(t)\Delta t^2 + O(4)$$
$$\vec x(t+\Delta t)=\vec x(t) + \vec x(t)-\vec x(t-\Delta t)+\frac{1}{2}\vec a(t)\,\Delta t^2+\frac{1}{2}\vec a(t)\,\Delta t^2 + O(4)$$
$$\vec x(t+\Delta t)=\vec x(t) + \widetilde{\vec{v}}(t) \Delta t +\frac{1}{2}\vec a(t)\,\Delta t^2 + O(4)$$
