Chapter 3 - Dynamics of Marine Vessels
Chapter 3 - Dynamics of Marine Vessels Chapter 3 - Dynamics of Marine Vessels
24 3.3.2 Linearized Equations of Motion Vessels in Transit (Cruise Condition): For vessels in transit the cruise speed is assumed to satisfy: u uo This suggests that where o uo,0,0,0,0,0 Nuo ∂ ∂ C D| o ̇ p Δ o MΔ̇ NuoΔ G p w Linear parameter varying (LPV) model: Auo ̇x Auox Bu Ew Fo 0 I −M−1G −M−1Nuo , B 0 M−1 , E 0 M−1 Δ − o x p ,Δ , F I 0 Ivar Ihle – TTK4190 Spring 2006
25 3.5 Standard Models for Marine Vessels Models for ships, semi-submersibles, and underwater vehicles are usually represented as one of the following subsystemes: or: Surge model: velocity u Maneuvering model (sway and yaw): velocities v and r Horizontal motion (surge, sway, and yaw): velocities u,v, and r Longitudinal motion (surge, heave, and pitch): velocities u,w, and q Lateral motion: (sway, roll, and yaw): velocities v,p, and r Horizontal plane models: DOFs 1, 2, 6 Longitudinal motion: DOFs 1, 3, 5 Lateral motion: DOFs 2, 4, 6 Ivar Ihle – TTK4190 Spring 2006
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24<br />
3.3.2 Linearized Equations <strong>of</strong> Motion<br />
<strong>Vessels</strong> in Transit (Cruise Condition):<br />
For vessels in transit the cruise speed is assumed to satisfy:<br />
u uo<br />
This suggests that<br />
where<br />
o uo,0,0,0,0,0 <br />
Nuo ∂<br />
∂ C D| o<br />
̇ p Δ o<br />
MΔ̇ NuoΔ G p w<br />
Linear parameter varying (LPV) model:<br />
Auo <br />
̇x Auox Bu Ew Fo<br />
0 I<br />
−M−1G −M−1Nuo , B <br />
0<br />
M−1 , E <br />
0<br />
M−1 Δ − o<br />
x p ,Δ <br />
, F <br />
I<br />
0<br />
Ivar Ihle – TTK4190 Spring 2006
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