Chapter 3 - Dynamics of Marine Vessels
Chapter 3 - Dynamics of Marine Vessels Chapter 3 - Dynamics of Marine Vessels
44 3.5.3 Longitudinal and Lateral Models Lateral Subsystem (DOFs 2, 4, 6) J R b n Θ TΘΘ R b n Θ 033 033 TΘΘ cc −sc css ss ccs sc cc sss −cs ssc −s cs cc 1 st ct 0 c −s 0 s/c c/c Resulting kinematic equation: ̇ p ̇ r u, w, p, r, and are small not controlling the E-position using heading control instead Ivar Ihle – TTK4190 Spring 2006
45 3.5.3 Longitudinal and Lateral Models Lateral Subsystem (DOFs 2, 4, 6) Again it is assumed that higher order velocity terms can be neglected so that Dn 0. Hence: CRB Collecting terms in v,p, and r, gives: CRB ≈ Assuming a diagonal M A gives: CA −my g p wp mz g r xgpq − my g r − ur −my g q z g ru my g p wv mz g p − vw −I yz q − I xz p I z rq I yz r Ixyp − I y qr mx g r vu my g r − uv − mx g p y g qw −I yz r − Ixyp I y qp I xz r Ixyq − I x pq 0 0 muo 0 0 0 0 0 mxguo Zẇ wp − X u̇ ur Y v̇ −Zẇ vw M q̇ −Nṙ qr X u̇ −Y v̇ uv K ṗ −Mq̇ pq v p r ≈ CRB ≠−CRB The skew-symmetric property is destroyed for the decoupled model: 0 0 −Xu̇ u 0 0 0 X u̇ −Y v̇ u 0 0 v p r Ivar Ihle – TTK4190 Spring 2006
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44<br />
3.5.3 Longitudinal and Lateral Models<br />
Lateral Subsystem (DOFs 2, 4, 6)<br />
J <br />
R b n Θ <br />
TΘΘ <br />
R b n Θ 033<br />
033 TΘΘ<br />
cc −sc css ss ccs<br />
sc cc sss −cs ssc<br />
−s cs cc<br />
1 st ct<br />
0 c −s<br />
0 s/c c/c<br />
Resulting kinematic equation:<br />
̇ p<br />
̇ r<br />
u, w, p, r, and are small<br />
not controlling the E-position<br />
using heading control instead<br />
Ivar Ihle – TTK4190 Spring 2006
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