ẋ = aq − (na/c) y, ẏ = −ap + (na/c) x.
(31)
Eliminating p, g, P, Q, we obtain the equations
(C + M0a2) ẍ + (Cna/c) y − (M0ga2/c) x = 0,
(C + M0a2) ÿ − (Cna/c) x − (M0ga2/c) y = 0,
(32)
which are both contained in
| { (C + M0a2) | d2 | − i | Cna | d | − | M0ga2 | } (x + iy) = 0. | |
| dt2 | c | dt | c |
(33)
This has two solutions of the type x + iy = αei(σt + ε), where α, ε are arbitrary, and σ is a root of the quadratic
(C + M0a2) σ2 − (Cna/c) σ + M0ga2/c = 0.