A half wave length of the curve of gyrostats is covered when ck = π, so that π/c is the number of gyrostats in a half wave, which is therefore of wave length 2π (a + l)/c.
A plane polarized wave is given when exp cki is replaced by exp (nt + ck) i, and a wave circularly polarized when w, ῶ, σ of § 14 replace this x, θ, α.
Gyroscopic Pendulum.—The elastic flexure joint is useful for supporting a rod, carrying a fly-wheel, like a gyroscopic pendulum.
Expressed by Euler’s angles, θ, φ, ψ, the kinetic energy is
T = ½A (θ2 + sin2 θψ2) + ½C′ (1 − cos θ)2ψ2 + ½C (φ + ψ cos θ)2,
(12)
where A refers to rod and gyroscope about the transverse axis at the point of support, C′ refers to rod about its axis of length, and C refers to the revolving fly-wheel.
The elimination of ψ between the equation of conservation of angular momentum about the vertical, viz.
(13) A sin2 θψ − C′ (1 − cos θ) cos θψ + C(φ + ψ cos θ) cos θ = G, a constant, and the equation of energy, viz.
(14) T − gMh cos θ = H, a constant, with θ measured from the downward vertical, and