(11)
become
m (ẍ − 2φ˙ẏ − xφ˙² − yφ¨) = X, m (ÿ + 2φ˙ẋ − yφ˙² + xφ¨) = Y, mz¨ = Z,
(12)
and
| d | [{I + m (x² + y²)} φ˙ + m (xẏ − yẋ)] = Φ. |
| dt |
(13)
If we suppose Φ adjusted so as to maintain φ¨ = 0, or (again) if we suppose the moment of inertia I to be infinitely great, we obtain the familiar equations of motion relative to moving axes, viz.
m (ẍ − 2ωẏ − ω²x) = X, m (ÿ + 2ωẋ − ω²y) = Y, mz¨ = Z,
(14)