Jerk (kinematics)
= Jerk
{disambiguate=kinematics}
{title2=$\mathbf j=d\mathbf a/dt=d^3\mathbf r/dt^3$}
{wiki=Jerk_(physics)}
= Kinematic jerk
{synonym}
The kinematic jerk is the time derivative of <acceleration>. For a <Kepler orbit> with relative position $\mathbf r$, relative velocity $\mathbf v$, $r=|\mathbf r|$, $\dot r=\mathbf r\cdot\mathbf v/r$ and total <mass> $M$, differentiation of <Newton's law of universal gravitation> gives $\mathbf j=-GM(\mathbf v-3\dot r\,\mathbf r/r)/r^3$.