About the Author xvii Preface xix List of Tables xxi Part One Marine Craft Hydrodynamics 1 Introduction to Part I 3 1.1 Classification of Models 6 1.2 The Classical Models in Naval Architecture 8 1.2.1 Maneuvering Theory 10 1.2.2 Seakeeping Theory 12 1.2.

3 Unified Theory 14 1.3 Fossen''s Robot-inspired Model for Marine Craft 14 2 Kinematics 17 2.1 Kinematic Preliminaries 18 2.1.1 Reference Frames 18 2.1.2 Body-fixed Reference Points 21 2.1.

3 Generalized Coordinates 22 2.2 Transformations Between BODY and NED 23 2.2.1 Euler Angle Transformation 26 2.2.2 Unit Quaternions 32 2.2.3 Unit Quaternion from Euler Angles 38 2.

2.4 Euler Angles from a Unit Quaternion 38 2.3 Transformations Between ECEF and NED 39 2.3.1 Longitude and Latitude Rotation Matrix 40 2.3.2 Longitude, Latitude and Height from ECEF Coordinates 41 2.3.

3 ECEF Coordinates from Longitude, Latitude and Height 44 2.4 Transformations between ECEF and Flat-Earth Coordinates 45 2.4.1 Longitude, Latitude and Height from Flat-Earth Coordinates 45 2.4.2 Flat-Earth Coordinates from Longitude, Latitude and Height 46 2.5 Transformations Between BODY and FLOW 47 2.5.

1 Definitions of Heading, Course and Crab Angles 47 2.5.2 Definitions of Angle of Attack and Sideslip Angle 49 2.5.3 Flow-axes Rotation Matrix 51 3 Rigid-body Kinetics 55 3.1 Newton-Euler Equations of Motion about the CG 56 3.1.1 Translational Motion About the CG 58 3.

1.2 Rotational Motion About the CG 59 3.1.3 Equations of Motion About the CG 60 3.2 Newton-Euler Equations of Motion About the CO 60 3.2.1 Translational Motion About the CO 61 3.2.

2 Rotational Motion About the CO 61 3.3 Rigid-body Equations of Motion 63 3.3.1 Nonlinear 6-DOF Rigid-body Equations of Motion 63 3.3.2 Linearized 6-DOF Rigid-body Equations of Motion 69 4 Hydrostatics 71 4.1 Restoring Forces for Underwater Vehicles 71 4.1.

1 Hydrostatics of Submerged Vehicles 71 4.2 Restoring Forces for Surface Vessels 74 4.2.1 Hydrostatics of Floating Vessels 74 4.2.2 Linear (Small Angle) Theory for Boxed-shaped Vessels 77 4.2.3 Computation of Metacenter Heights for Surface Vessels 79 4.

3 Load Conditions and Natural Periods 82 4.3.1 Decoupled Computation of Natural Periods 82 4.3.2 Computation of Natural Periods in a 6-DOF Coupled System 84 4.3.3 Natural Periods as a Function of Load Condition 87 4.3.

4 Free-surface Effects 89 4.3.5 Payload Effects 90 4.4 Seakeeping Analysis 90 4.4.1 Harmonic Oscillator with Sinusoidal Forcing 90 4.4.2 Steady-state Heave, Roll and Pitch Responses in Regular Waves 92 4.

4.3 Explicit Formulae for Boxed-shaped Vessels in Regular Waves 94 4.4.4 Case Study: Resonances in the Heave, Roll and Pitch Modes 96 4.5 Ballast Systems 97 4.5.1 Static Conditions for Trim and Heel 99 4.5.

2 Automatic Ballast Control Systems 102 5 Seakeeping Models 105 5.1 Hydrodynamic Concepts and Potential Theory 106 5.1.1 Numerical Approaches and Hydrodynamic Codes 108 5.2 Seakeeping and Maneuvering Kinematics 110 5.2.1 Seakeeping Reference Frame 110 5.2.

2 Transformation Between BODY and SEAKEEPING 111 5.3 The Classical Frequency-domain Model 114 5.3.1 Frequency-dependent Hydrodynamic Coefficients 115 5.3.2 Viscous Damping 119 5.3.3 Response Amplitude Operators 121 5.

4 Time-domain Models including Fluid Memory Effects 122 5.4.1 Cummins Equation in SEAKEEPING Coordinates 122 5.4.2 Linear Time-domain Seakeeping Equations in BODY Coordinates 125 5.4.3 Nonlinear Unified Seakeeping and ManeuveringModel with Fluid Memory Effects 129 5.5 Identification of Fluid Memory Effects 130 5.

5.1 Frequency-domain Identification Using the MSS FDI Toolbox 131 6 Maneuvering Models 135 6.1 Rigid-body Kinetics 137 6.2 Potential Coefficients 137 6.2.1 Frequency-independent Added Mass and Potential Damping 139 6.2.2 Extension to 6-DOF Models 140 6.

3 Added Mass Forces in a Rotating Coordinate System 141 6.3.1 Lagrangian Mechanics 142 6.3.2 Kirchhoff''s Equation 143 6.3.3 Added Mass and Coriolis-Centripetal Matrices 143 6.4 Dissipative Forces 148 6.

4.1 Linear Damping 150 6.4.2 Nonlinear Surge Damping 151 6.4.3 Cross-flow Drag Principle 154 6.5 Ship Maneuvering Models (3 DOFs) 155 6.5.

1 Nonlinear Equations of Motion 155 6.5.2 Nonlinear Maneuvering Model Based on Surge Resistance and Cross-flow Drag 158 6.5.3 Nonlinear Maneuvering Model Based on Second-order Modulus Functions 159 6.5.4 Nonlinear Maneuvering Model Based on Odd Functions 161 6.5.

5 Linear Maneuvering Model 163 6.6 Ship Maneuvering Models Including Roll (4 DOFs) 165 6.6.1 The Nonlinear Model of Son and Nomoto 172 6.6.2 The Nonlinear Model of Blanke and Christensen 173 6.7 Low-Speed Maneuvering Models for Dynamic Positioning (3 DOFs) 175 6.7.

1 Current Coefficients 175 6.7.2 Nonlinear DP Model Based on Current Coefficients 179 6.7.3 Linear Time-varying DP Model 180 7 Autopilot Models for Course and Heading Control 183 7.1 Autopilot Models for Course Control 184 7.1.1 State-space Model for Course Control 184 7.

1.2 Course Angle Transfer Function 185 7.2 Autopilot Models for Heading Control 186 7.2.1 Second-order Nomoto Model 186 7.2.2 First-order Nomoto Model 188 7.2.

3 Nonlinear Extensions of Nomoto''s Model 190 7.2.4 Pivot Point 192 8 Models for Underwater Vehicles 195 8.1 6-DOF Models for AUVs and ROVs 195 8.1.1 Equations of Motion Expressed in BODY 195 8.1.2 Equations of Motion Expressed in NED 197 8.

1.3 Properties of the 6-DOF Model 198 8.1.4 Symmetry Considerations of the System Inertia Matrix 200 8.2 Longitudinal and Lateral Models for Submarines 201 8.2.1 Longitudinal Subsystem 202 8.2.

2 Lateral Subsystem 204 8.3 Decoupled Models for "Flying Underwater Vehicles" 205 8.3.1 Forward Speed Subsystem 206 8.3.2 Course Angle Subsystem 206 8.3.3 Pitch-Depth Subsystem 207 8.

4 Cylinder-Shaped Vehicles and Myring-type Hulls 208 8.4.1 Myring-type Hull 209 8.4.2 Spheroid Approximation 210 8.5 Spherical-Shaped Vehicles 214 9 Control Forces and Moments 217 9.1 Propellers as Thrust Devices 217 9.1.

1 Fixed-pitch Propeller 217 9.1.2 Controllable-pitch Propeller 220 9.2 Ship Propulsion Systems 225 9.2.1 Podded Propulsion Units 225 9.2.2 Prime Mover System 227 9.

3 USV and Underwater Vehicle Propulsion Systems 228 9.3.1 Propeller Shaft Speed Models 229 9.3.2 Motor Armature Current Control 230 9.3.3 Motor Speed Control 232 9.4 Thrusters 233 9.

4.1 Tunnel Thrusters 233 9.4.2 Azimuth Thrusters 234 9.5 Rudder in the Propeller Slipstream 236 9.5.1 Rudder Forces and Moment 237 9.5.

2 Steering Machine Dynamics 240 9.6 Fin Stabilizators 243 9.6.1 Lift and Drag Forces on Fins 244 9.6.2 Roll Moment Produced by Symmetrical Fin Stabilizers 245 9.7 Underwater Vehicle Control Surfaces 245 9.7.

1 Rudder 247 9.7.2 Dive Planes 248 9.8 Control Moment Gyroscope 249 9.8.1 Ship Roll Gyrostabilizer 249 9.8.2 Control Moment Gyros for Underwater Vehicles 252 9.

9 Moving Mass Actuators 258 10 Environmental Forces and Moments 261 10.1 Wind Forces and Moments 263 10.1.1 Wind Forces and Moments on Marine Craft at Rest 263 10.1.2 Wind Forces and Moments on Moving Marine Craft 265 10.1.3 Wind Coefficients Based on Helmholtz-Kirchhoff Plate Theory 266 10.

1.4 Wind Coefficients for Merchant Ships 269 10.1.5 Wind Coefficients for Very Large Crude Carriers 271 10.1.6 Wind Coefficients for Large Tankers and Medium-sized Ships 272 10.1.7 Wind Coefficients for Moored Ships and Floating Structures 272 10.

2 Wave Forces and Moments 274 10.2.1 Sea-state Descriptions 275 10.2.2 Wave Spectra 276 10.2.3 Wave Amplitude Response Model 287 10.2.

4 Force RAOs 290 10.2.5 Motion RAOs 293 10.2.6 State-space Models for Wave Response Simulation 296 10.3 Ocean Current Forces and Moments 300 10.3.1 3D Irrotational Ocean Current Model 303 10.

3.2 2D Irrotational Ocean Current Model 304 Part Two Motion Control 11 Introduction to Part II 309 11.1 Guidance, Navigation and Control Systems 310 11.1.1 Historical Remarks 312 11.1.2 Autopilots 314 11.1.

3 Dynamic Positioning and Position Mooring Systems 315 11.1.4 Waypoint Tracking and Path-following Control Systems 316 11.2 Control Allocation 316 11.2.1 Propulsion and Actuator Models 318 11.2.2 Unconstrained Control Allocation 322 11.

2.3 Constrained Control Allocation 324 12 Guidance Systems 331 12.1 Trajectory Tracking 333 12.1.1 Reference Models for Trajectory Generation 334 12.1.2 Trajectory Generation using a Marine Craft Simulator 339 12.1.

3 Optimal Trajectory Generation 340 12.2 Guidance Laws for Target Tracking 341 12.2.1 Line-of-sight Guidance Law 342 12.2.2 Pure-pursuit Guidance Law 343 12.2.3 Constant Bearing Guidance Law 344 12.

3 Linear Design Methods for Path Following 346