Introduction to Space Dynamics by William Tyrrell Thomson

Author:William Tyrrell Thomson
Language: eng
Format: epub
ISBN: 9780486140520
Publisher: Dover Publications
Published: 2012-07-17T16:00:00+00:00

(6.5–3)

Fig. 6.5-1. Vector components for the gyrocompass.

Eliminating ψ between these equations, the differential equation for α becomes

(6.5–4)

with the general solution,

(6.5–5)

(6.5–6)

From Eq. 6.5–3, the equation for ψ is,

(6.5–7)

These equations indicate that the spin axis oscillates horizontally about the meridian plane and vertically about the stationary angle α0, given by Eq. 6.4–3. The frequency of oscillation, Eq. 6.5–6 is a function of the latitude λ, and is very small due to in the denominator. The frequency p approaches zero, as the gyrocompass nears the north polar axis, where the reliability of the instrument diminishes.

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