while U′2 in (27) will not be positive and the straight chain will be unstable unless the tension exceeds
(κn + αn2) (1 + l/a).
(29)
15. Gyrostat suspended by a Thread.—In the discussion of the small vibration of a single gyrostat fly-wheel about the vertical position when suspended by a single thread of length 2l = b, the suffix k can be omitted in the preceding equations of § 14, and we can write
Aῶ − Kῶi + Taῶ − Taσ = 0,
(1)
Mw + Tσ = 0, with T = gM,
(2)
w − aῶ − bσ = 0.
(3)