ImPl Ul4KIcD2 2Ic

For f—>00, the steady-state solution, the first two terms on the right-hand side of Eq. (F-31) dominate 0(t). These two terms may be rewritten as sinu.r

ICAL \[ % \ Dut lim 0(t)= —--——----— I -—u, |cos«./+ -7—si

where

Du, K-Icut

Several features of gyroscope design are evident from these equations:

1. The output response of the system to a constant or low-frequency input, is linearly related to the input for /3>t0; for example, lim 0(t)=A{L/K) (/»t0) <i),-»0

2. The viscous damping constant, D; mjujst be sufficiently high so that r0 is small compared with the gyro sampling period. However, if the damping is too high, the system output becomes frequency dependent and lags the input.

3. Systems with negligible damping, Daa0, resonate at input frequencies near the characteristic frequency of the system,

Integral Equations. Integral equations have the general form

0 0

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