+ Aμ2 cos γ sin θ cos θ cos φ − (Kμ + gMh) sin θ cos φ = 0.
(11)
The position of relative equilibrium is given by
| cos φ = 0, and sin φ = | Kμ + gMh − Aμ2 cos γ cos θ | . |
| Aμ2 sin γ sin θ |
(12)
For small values of μ the equation becomes
| A | d2φ | sin γ − (Kμ + gMh) sin θ cos φ = 0, |
| dt2 |
(13)
so that φ = ½π gives the position of stable equilibrium, and the period of a small oscillation is 2π √{A sin γ/(Kμ + gMh) sin θ}.
In the general case, denoting the periods of vibration about φ = ½π, −½π, and the sidelong position of equilibrium by 2π/(n1, n2, or n3), we shall find