Chapter 3 - Dynamics of Marine Vessels
Chapter 3 - Dynamics of Marine Vessels Chapter 3 - Dynamics of Marine Vessels
32 3.5.2 Decoupled Models for Forward Speed/Maneuvering 2 DOF Linear Maneuvering Model (Sway-Yaw Subsystem) A linear maneuvering model is based on the assumption that the cruise speed: u uo ≈ constant while v and r are assumed to be small. Representation 1 (see also lecture notes by Professor David Clark) The 2nd and 3rd rows in the DP model with u=u o , yields: C C 0 0 − m − Y v̇ v − mx g −Yṙ r 0 0 m − X u̇ u m − Y v̇ v mx g −Y ṙ r −m − X u̇ u 0 m − X u̇ u o r m − Y v̇ u o v mx g −Y ṙ u o r − m − X u̇ u o v 0 m − X u̇ u o X u̇ −Yv̇ u o mx g −Y ṙ u o v r Notice that C ≠−C Ivar Ihle – TTK4190 Spring 2006
33 3.5.2 Decoupled Models for Forward Speed/Maneuvering Assume that the ship is controlled by a single rudder: and that linear damping dominates: then: where v, r b −Y −N D D D n ≈ D Ṁ Nuo b This is the linear maneuvering model as used by Clark, Fossen and others. Developed from M RB , C RB , M A , C A Notice: N includes the famous Munk moment and some other C A -terms M Nuo b m − Yv̇ mxg−Yṙ mxg−Y ṙ −Yv Iz−Nṙ m − X u̇ u o −Yr X u̇ −Yv̇ u o −Nv mx g −Y ṙ u o −Nr −Y −N Ivar Ihle – TTK4190 Spring 2006
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32<br />
3.5.2 Decoupled Models for Forward<br />
Speed/Maneuvering<br />
2 DOF Linear Maneuvering Model (Sway-Yaw Subsystem)<br />
A linear maneuvering model is based on the assumption that the cruise speed:<br />
u uo ≈ constant<br />
while v and r are assumed to be small.<br />
Representation 1 (see also lecture notes by Pr<strong>of</strong>essor David Clark)<br />
The 2nd and 3rd rows in the DP model<br />
with u=u o , yields:<br />
C <br />
C <br />
<br />
0 0 − m − Y v̇ v − mx g −Yṙ r<br />
0 0 m − X u̇ u<br />
m − Y v̇ v mx g −Y ṙ r −m − X u̇ u 0<br />
m − X u̇ u o r<br />
m − Y v̇ u o v mx g −Y ṙ u o r − m − X u̇ u o v<br />
0 m − X u̇ u o<br />
X u̇ −Yv̇ u o mx g −Y ṙ u o<br />
v<br />
r<br />
Notice that<br />
C ≠−C <br />
Ivar Ihle – TTK4190 Spring 2006
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