Analysis Used in Submerged Body Research 439 
where 
is the amplitude of the linear acceleration. 
Similarly, the reduction equations for the case of pure sideslipping (lateral translatory 
motion), as presented in Table 2, can be derived. 
PURE PITCHING MOTION 
The condition for pure pitching, as studied in Appendix A, is satisfied when the angle 
of attack 2, measured at the CG, is equal to zero at all times. For this condition, the re- 
sultant linear velocity w and linear acceleration w are zero. The pitch angle, pitching ve- 
locity, and pitching acceleration can be expressed as 
tei Peds Taedin chu 9a). Pe de 
@= ep aT ee sin 2a cos |at - ba ’ (B19) 
the angular velocity as 
BS q= -0(22 sin = |- sin (oe - $2) ], (B20) 
and the angular acceleration as 
ahs der é t, 
PSM ge var (22 sin £3 lee (wt = fs), (B21) 
where 
2 =) 
B sin > 
is the maximum amplitude of the pitch angle 0,. 
Substituting Eqs. (B19), (B20), and (B21) in Eqs. (B2) and (B4) yields: 
= | é, 
- a (22 sin >) (5 pez. + n.,) - sin (.t - = +Z, (B22) 
