— sin ^ cos <p + cos ^ sin 0 sin <p sin ^ sin <p + cos ^ sin 0 cos ^
cos ^ cos ^ + sin ^ sin 0 sin ^ — cos ^ sin ^ + sin ^ sin 0 cos ^ cos 0 sin ^ cos 0 cos ^
2.4 UV dynamic model
Dynamic mathematical model of underwater vehicles is coupled and nonlinear. General model equation is given with (3).
Matrix M = MRB + MA presents the sum of rigid body and added mass matrices, matrix D(v) is drag (usually diagonal and has linear and quadratic terms), matrix C(v) = CRB(v) + CA(v) is a sum of Coriolis forces rigid body and added mass matrices, while vector contains gravitational and lift forces. Vector T contains external forces and moments acting upon the underwater vehicle and T^ is the disturbance vector.
From here on we will assume that the only controllable degrees of freedom are surge, yaw and heave, and that sway can appear due to coupling. These assumptions do not limit the applicability of the proposed methods but only simplify them. Coupled model in the horizontal plane m — Xü
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