of which the last two express the constancy of the momenta μ, ν. Hence
Aθ̈ − A sin θ cos θψ̇2 + ν sin θψ̇ = Mgh sin θ,
A sin2 θψ̇ + ν cosθ = μ.
(29)
If we eliminate ψ̇ we obtain the equation (7) of § 20. The theory of disturbed precessional motion there outlined does not give a convenient view of the oscillations of the axis about the vertical position. If θ be small the equations (29) may be written
| θ̈ − θω̇2 = − | ν2 − 4AMgh | θ, |
| 4A2 |
θ2ω̇ = const.,
(30)
where
| ω = ψ − | ν | t. |
| 2A |
(31)