Chapter 3 - Dynamics of Marine Vessels
Chapter 3 - Dynamics of Marine Vessels Chapter 3 - Dynamics of Marine Vessels
14 Pitch angle (deg) 3.2.4 Ballast Systems Roll and pitch angles during lift-off roll roll and pitch (deg) pitch 4.21 A 1 < > jp 0.95 5.5 6 4.5 5 3.5 4 2.5 3 1.5 2 0.5 1 0.5 0 1.5 1 6 4 2 0 2 0 187.5 375 562.5 750 937.5 1125 1312.5 1500 2 420 430 440 450 460 470 420 jp time (secs) Measured pitch during launch Roll and pitch during launch 470 pitch angle (deg) 4.326 Z 4 < > . 180 l π 0.202 6 4 2 0 2 time (secs) 20 10 0 10 20 30 15 Z time (secs) 1 < > l Calculated pitch motions 29.775 Ivar Ihle – TTK4190 Spring 2006
15 3.3 6 DOF Equations of Motion Body-Fixed Vector Representation M ̇ C D g g o w ̇ J M MRB MA C CRB CA D DP DS DW DM NED Vector Representation Kinematic transformation (assuming that J exists-i.e., ): −1 ≠ /2 ̇ J J−1 ̇ ̈ J ̇ ̇J ̇ J−1̈ − ̇JJ −1 ̇ M ∗ J − M J −1 C ∗ , J − C − MJ −1 ̇JJ −1 D∗, J− D J−1 g∗ J− g M ∗ ̈ C ∗ , ̇ D ∗ , ̇ g ∗ J − g o w Ivar Ihle – TTK4190 Spring 2006
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- Page 17 and 18: 17 3.3.1 Nonlinear Equations of Mot
- Page 19 and 20: 19 3.3.2 Linearized Equations of Mo
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- Page 27 and 28: 27 3.5.1 3 DOF Horizontal Motion Lo
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- Page 31 and 32: 31 3.5.2 Decoupled Models for Forwa
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14<br />
Pitch angle (deg)<br />
3.2.4 Ballast Systems<br />
Roll and pitch angles during lift-<strong>of</strong>f<br />
roll<br />
roll and pitch (deg)<br />
pitch<br />
4.21<br />
A 1 < > jp<br />
0.95<br />
5.5 6<br />
4.5 5<br />
3.5 4<br />
2.5 3<br />
1.5 2<br />
0.5 1<br />
0.5 0<br />
1.5 1<br />
6<br />
4<br />
2<br />
0<br />
2<br />
0 187.5 375 562.5 750 937.5 1125 1312.5 1500<br />
2<br />
420 430 440 450 460 470<br />
420 jp<br />
time (secs)<br />
Measured pitch during launch<br />
Roll and pitch during launch<br />
470<br />
pitch angle (deg)<br />
4.326<br />
Z 4 < > . 180<br />
l<br />
π<br />
0.202<br />
6<br />
4<br />
2<br />
0<br />
2<br />
time (secs)<br />
20 10 0 10 20 30<br />
15<br />
Z<br />
time (secs)<br />
1 < > l<br />
Calculated pitch motions<br />
29.775<br />
Ivar Ihle – TTK4190 Spring 2006
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