= Solution
At <latitude> $\ell$, the Earth's angular <velocity> in east–north–up coordinates is $\boldsymbol\Omega=(0,\Omega\cos\ell,\Omega\sin\ell)$. Assume a small horizontal patch, constant $\Omega$, negligible vertical <velocity>, and a vertical constraint balancing effective <gravity>. Absorb the steady <centrifugal force> into that effective <gravity>. With $f=2\Omega\sin\ell$ and physical horizontal <force> per unit mass $F_x',F_y'$, the <Coriolis force> gives
$$
\boxed{\ddot x'=f\dot y'+F_x',\qquad\ddot y'=-f\dot x'+F_y',\quad A=D=0,\ B=f,\ C=-f.}
$$
Large-scale atmospheric and oceanic flows deflect to their right in the northern hemisphere and left in the southern hemisphere; their balance with a horizontal <pressure gradient> produces <geostrophic flow>. A <Foucault pendulum> has an oscillation plane that precesses relative to the ground at angular rate $-\Omega\sin\ell$. Both effects vanish at the equator within this horizontal approximation.
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