Chapter 3 - Dynamics of Marine Vessels

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3.5.3 Longitudinal and Lateral Models
Longitudinal Subsystem (DOFs 1, 3, 5)
For simplicity, it is assumed that higher order damping can be neglected, that is
Dn 0. Coriolis is, however, modelled by assuming that u 0 and that
2nd-order terms in v,w,p,q, and r are small. Hence, DOFs 1, 3, 5 gives:
CRB
CRB ≈
my g q z g rp − mx g q − wq − mx g r vr
−mz g p − vp − mz g q uq mx g p y g qr
mx g q − wu − mz g r xgpv mz g q uw I yz q I xz p − I z rp −I xz r − Ixyq I x pr
Collecting terms in u,w, and q, gives:
0 0 0
0 0 −mu
0 0 mxgu
Assuming a diagonal M A gives:
CA
−Zẇ wq Y v̇ vr
−Y v̇ vp X u̇ uq
u
w
Z ẇ −Xu̇ uw N ṙ −Kṗ pr
q
≈
0 0 0
0 0 Xu̇ u
0 Z ẇ −Xu̇ u 0
CRB ≠−CRB
The skew-symmetric property is
destroyed for the decoupled model:
u
w
q
Ivar Ihle – TTK4190 Spring 2006