Davis and Oates 



y = lateral axis 



Z = vertical forces (along z axis) (lb) 



z = vertical axis 



z(t,z) = instantaneous sea surface elevation 



z^, z^.zjj, zp = wave amplitudes (ft) 



a = angle of attack 



a^ = steady- state angle of attack 



a^ = djmamic angle of attack 



/3 = sideslip angle 



r = dihedral angle (degrees) 



$ = roll angle in Euler equation I 



$ = phase angle (regular seas) (radians) 



0(f,x) = spectral density of wave surface elevation (ft^/cycle/sec) 



<D^(f) = Neumann power spectral density function (random seas) 

 (ft Vcycle/sec) 



(p = randomly chosen phase angle (random seas) (radians) 



4> = roll angle (radians) 



= rolling velocity (d^/dt) (radians/sec) 



4> = rolling acceleration (dV/dt^) (radians/sec) 



k = wave length (ft) 



fi = nondimensional relative density parameter m/pS^s 



p = fluid mass density (slugs/cu ft) 



r = integrator time constant 



= yaw angle (radians) 



oj = angular rate (rads/sec) 



o) = wave frequency (rads/sec) 



c^' = frequency of encounter (rads/sec) 



650 



