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Admittance for the Moment
The yawing moment can be calculated around any axis a (Filippone and Siquier, 2003), and is written as:
#AMW= (a + 0 [МЩ – iJl(k)]C(k)
i 1 — A
– — (A + 2a)Ji(Afe)-— J2(Xk) (11)
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where J2 is a Bessel function of order 2. A number of simplifications can be made from Eq. 11. First, consider a body pitching or yawing around an axis a = -1/2. In this case, Eq. 11 can be simplified in at least two cases: If a = -1/2, then
1 (stationary gust), then
Hjf=i(k) = (a+^Hx=1(k). (13)
Therefore, the admittance for the yawing moment is proportional to the admittance for the side force, and the two functions are in phase at all frequencies.
The latter equation can be normalized so as to have a unit value at k ~ 1. Also note that if a = -1/2 then the body is neutral at all frequencies with respect to the pitching moment.
