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For a frame rotating with constant angular velocity $\boldsymbol\omega$,
$$
\mathbf a_{\rm inertial}
=\ddot{\mathbf x}+2\boldsymbol\omega\times\dot{\mathbf x}
+\boldsymbol\omega\times(\boldsymbol\omega\times\mathbf x).
$$
The extra terms produce the Coriolis and centrifugal forces in the rotating-frame equation.


Equation of motion in a rotating frame

Hill equations

Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 4 / 12A / Solution

Equation of motion in a rotating frame

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Equation of motion in a rotating frame

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