| 2T = Ma2θ̇2 + m (aθ̇ + bψ̇)2 |
| 2V = Mgaθ2 + mg (aθ2 + bψ2). |
(9)
The equations (3) take the forms
| aθ ̈ + μbφ̈ + gθ = 0, |
| aθ ̈ + bφ̈ + gφ = 0. |
(10)
where μ = m/(M + m). Hence
| (σ2 − g/a) aθ + μσ2bφ = 0, |
| σ2aθ + (σ2 − g/b) bφ = 0. |
(11)
The frequency equation is therefore
(σ2 − g/a) (σ2 − g/b) − μσ4 = 0.