Chapter 3 - Dynamics of Marine Vessels
Chapter 3 - Dynamics of Marine Vessels
Chapter 3 - Dynamics of Marine Vessels
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28<br />
3.5.1 3 DOF Horizontal Motion<br />
Assume that the ship has homogeneous mass distribution, xz-plane symmetry and y g =0:<br />
MRB <br />
MA −<br />
m 0 0 0 mzg −my g<br />
0 m 0 −mzg 0 mxg<br />
0 0 m my g −mxg 0<br />
0 −mzg my g Ix −Ixy −Ixz<br />
mzg 0 −mxg −Iyx Iy −Iyz<br />
X<br />
−my g mxg 0 −Izx −Izy Iz<br />
Xu̇ Xv̇ Xẇ Xṗ Xq̇ Xṙ<br />
X<br />
Yu̇ Yv̇ Yẇ Yṗ Yq̇ Yṙ<br />
Zu̇ Zv̇ Zẇ Zṗ Zq̇ Zṙ<br />
Ku̇ Kv̇ Kẇ Kṗ Kq̇ Kṙ<br />
Mu̇ Mv̇ Mẇ Mṗ Mq̇ Mṙ<br />
X<br />
X<br />
X<br />
Nu̇ Nv̇ Nẇ Nṗ Nq̇ Nṙ<br />
X<br />
MRB <br />
CRB <br />
MA <br />
CA <br />
m 0 0<br />
0 m mxg<br />
0 mxg Iz<br />
0 0 −mx g r v<br />
0 0 mu<br />
mx g r v −mu 0<br />
−Xu̇ 0 0<br />
0 −Y v̇ −Y ṙ<br />
0 −Yṙ −Nṙ<br />
0 0 Y v̇ v Y ṙ r<br />
0 0 −Xu̇ u<br />
−Yv̇ v − Y ṙ r Xu̇ u 0<br />
Ivar Ihle – TTK4190 Spring 2006
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