1. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space J. Offshore Mech. Arct. Eng. 2012;134(3):031903-031903-8. doi:10.1115/1.4004630 Coordinate systems (X,Y,Z), (x,y,z), and (A,B,C) and Euler angles(θ1,θ2,η). Axis A shown slightly offset from z for clarity. Figure Legend:

2. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space J. Offshore Mech. Arct. Eng. 2012;134(3):031903-031903-8. doi:10.1115/1.4004630 Rotation of (A,B,C) in terms ofφ,θ, andψ Figure Legend:

3. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space J. Offshore Mech. Arct. Eng. 2012;134(3):031903-031903-8. doi:10.1115/1.4004630 Projection of Euler angular velocities Figure Legend:

4. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space J. Offshore Mech. Arct. Eng. 2012;134(3):031903-031903-8. doi:10.1115/1.4004630 Coordinate system for derivation of inertial and environmental forcing Figure Legend:

5. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space J. Offshore Mech. Arct. Eng. 2012;134(3):031903-031903-8. doi:10.1115/1.4004630 Case 1: Free vibration described by three Euler angles Figure Legend:

6. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space J. Offshore Mech. Arct. Eng. 2012;134(3):031903-031903-8. doi:10.1115/1.4004630 Case 1: Comparison ofωX Figure Legend:

7. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space J. Offshore Mech. Arct. Eng. 2012;134(3):031903-031903-8. doi:10.1115/1.4004630 Case 1: Comparisons ofωYandωZ Figure Legend:

8. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space J. Offshore Mech. Arct. Eng. 2012;134(3):031903-031903-8. doi:10.1115/1.4004630 Precession angle of the RNA Figure Legend:

9. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space J. Offshore Mech. Arct. Eng. 2012;134(3):031903-031903-8. doi:10.1115/1.4004630 Gyro moments acting on the RNA Figure Legend: