Chapter 3 - Dynamics of Marine Vessels

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34 3.5.2 Decoupled Models for Forward Speed/Maneuvering 2 DOF Linear Maneuvering Model (Sway-Yaw Subsystem) Representation 2 (Davidson and Schiff 1946). Starts with Newton’s law: where linear terms in acceleration, velocity and rudder are added according to: Notice: This approach does not included the C A -matrix. The resulting model is: M MRḂ CRB RB RB − Y N m − Yv̇ mxg−Yṙ mxg−Y ṙ Iz−Nṙ Yv̇ Yṙ Nv̇ Nṙ Ṁ Nuo b , Nuo In this model the Munk moment is missing in the yaw equation. This is a destabilizing moment known from aerodynamics which tries to turn the vessel. Also notice that two other less important C A -terms are removed from N(u o ) when compared to Representation 1. ̇ −Yv Yv Yr Nv Nr muo−Y r −Nv mxguo−Nr , b −Y −N Ivar Ihle – TTK4190 Spring 2006
35 3.5.2 Decoupled Models for Forward Speed/Maneuvering 1 DOF Autopilot Model (Yaw Subsystem) A linear autopilot model for course control can be derived from the maneuvering model Ṁ Nuo b by defining the yaw rate r as output: r c , c 0, 1 Hence, application <strong>of</strong> the Laplace transformation yields (Nomoto 1957): r s The 1st-order Nomoto model is obtained by defining the equivalent time constant as: T T1 T2 − T3 r s K 1Ts K1T3s 1T1s1T2s 2nd-order Nomoto model ̇ r s K s1Ts Ivar Ihle – TTK4190 Spring 2006
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Page 3 and 4: 3 3.2.4 Ballast Systems Consider a
Page 5 and 6: 5 3.2.4 Ballast Systems Conditions
Page 7 and 8: 7 3.2.4 Ballast Systems Example (Se
Page 9 and 10: 9 3.2.4 Ballast Systems Automatic P
Page 11 and 12: 11 3.2.4 Ballast Systems Feedback c
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Page 15 and 16: 15 3.3 6 DOF Equations of Motion Bo
Page 17 and 18: 17 3.3.1 Nonlinear Equations of Mot
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Page 27 and 28: 27 3.5.1 3 DOF Horizontal Motion Lo
Page 29 and 30: 29 3.5.1 3 DOF Horizontal Motion Fo
Page 31 and 32: 31 3.5.2 Decoupled Models for Forwa
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Chapter 3 - Dynamics of Marine Vessels

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