= Translating accelerated reference frame
{title2=$m\ddot{\mathbf R}=\mathbf F-m\ddot{\mathbf a}$}
If the origin of a nonrotating <reference frame> has inertial <position> $\mathbf a(t)$ and a particle has relative <position> $\mathbf R$, then $\mathbf r=\mathbf R+\mathbf a$. <Newton's second law> becomes $m\ddot{\mathbf R}=\mathbf F-m\ddot{\mathbf a}$. The effective inertial <force> is therefore $-m\ddot{\mathbf a}$. No rotation-dependent terms arise because the coordinate axes remain parallel to the inertial axes.
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