(19)
R { −(A1 + M1h12 + Mb2) n2 + K1n + g (M1h1 + Mb)} − PMn2ab2 = 0.
(20)
Eliminating the ratio of P to R, we obtain
| { −(A + Ma2) n2 + Kn + gMa} × { −(A1 + M1h12 + Mb2) n2 + K1n + g (M1h1 + Mb)} − M2n4a2b2 = 0, |
(21)
a quartic for n, giving the frequency n/2π of a fundamental vibration.
Change the sign of g for the case of the gyrostats spinning upright, one on the top of the other, and so realize the gyrostat on the top of a gyrostat described by Maxwell.
In the gyrostatic chain of § 14, the tension T may change to a limited pressure, and U2 may still be positive, and the motion stable; and so a motion is realized of a number of spinning tops, superposed in a column.
16. The Flexure Joint.—In Lord Kelvin’s experiment the gyrostats are joined up by equal light rods and short lengths of elastic wire with rigid attachment to the rod and case of a gyrostat, so as to keep the system still, and free from entanglement and twisting due to pivot friction of the fly-wheels.