Chapter 3 - Dynamics of Marine Vessels
Chapter 3 - Dynamics of Marine Vessels Chapter 3 - Dynamics of Marine Vessels
46 3.5.3 Longitudinal and Lateral Models Lateral Subsystem (DOFs 2, 4, 6) The restoring forces with W=B, xg =xb and yg =zg : g g − W − B sin W − B cos sin − W − B cos cos − ygW − ybB cos cos zgW − zbB cos sin z g W − zbB sin x g W − xbB cos cos − x g W − xbB cos sin − y g W − y b B sin 0 WBGzsin 0 Ivar Ihle – TTK4190 Spring 2006
47 3.5.3 Longitudinal and Lateral Models Lateral Subsystem (DOFs 2, 4, 6) m − Yv̇ −mzg − Yṗ mxg − Yṙ −mzg − Yṗ Ix − Kṗ −Izx − Kṙ mxg − Yṙ −Izx − Kṙ Iz − Nṙ 0 0 m − Xu̇ u 0 0 0 Xu̇ − Yv̇ u 0 mxgu u uo constant m − Yv̇ mxg−Yṙ mxg−Y ṙ Iz−Nṙ v̇ ṙ 0 m − X u̇ u o X u̇ −Y v̇ u o mxguo v p r v̇ ṗ ṙ −Yv −Yr −Nv −Nr v r −Yv −Yp −Yr −Mv −Mp −Mr −Nv −Np −Nr 0 WBGzsin 0 v r 2 6 2 4 6 v p r Ivar Ihle – TTK4190 Spring 2006
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46<br />
3.5.3 Longitudinal and Lateral Models<br />
Lateral Subsystem (DOFs 2, 4, 6)<br />
The restoring forces with W=B, xg =xb and yg =zg :<br />
g <br />
g <br />
−<br />
W − B sin<br />
W − B cos sin<br />
− W − B cos cos<br />
− ygW − ybB cos cos zgW − zbB cos sin<br />
z g W − zbB sin x g W − xbB cos cos<br />
− x g W − xbB cos sin − y g W − y b B sin<br />
0<br />
WBGzsin 0<br />
Ivar Ihle – TTK4190 Spring 2006
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