1. Date of download: 10/22/2017
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From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
A supercavitating vehicle body with an envelope surrounding it

2. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Forces acting on a supercavitating vehicle

3. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Depiction of immersion depth

4. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Closed-loop system response for delay dependent system with initial condition (w0,q0,θ0,z0)=(2.4,0,0.03,0) and δc=-0.3q-30θ+15z, δe=0. Here, V=80 m/s.

5. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Planing force as a function of time for the closed-loop delay-free system with δc=-0.3q-30θ+15z, δe=0

6. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Closed-loop system response for delay dependent system with initial condition (w0,q0,θ0,z0)=(2.4,0,0.03,0) and δc=-0.3q-30θ+15z, δe=0. Here, V=80 m/s.

7. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Planing force as a function of time for the closed-loop delay dependent system with δc=-0.3q-30θ+15z, δe=0

8. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Closed-loop system response for delay-free model with zero initial condition and δc=-0.3q-30θ+15z, δe=0. Here, V=87 m/s.

9. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Effect of delay on stable equilibrium point. Delay is increased from 0 to 0.025s in steps of s. The stable equilibrium point looses stability and a limit cycle is born around τ=0.0013s.

10. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Closed-loop system response for delay-dependent system with control δc=-0.3q-10θ+130z, δe=-0.1 (stabilization outside cavity). Here, V=87 m/s.

11. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Cavitator and elevator deflection angles as a function of time for the closed-loop system with control δc=-0.3q-10θ+130z, δe=-0.1 (stabilization outside cavity). Here, V=87 m/s.

12. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Planing force as a function of time for the closed-loop system with control δc=-0.3q-10θ+130z, δe=-0.1 (stabilization outside cavity). Here, V=87 m/s. Note that the value of the (normalized) planing force approaches a nonzero constant.

13. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Closed-loop system response for delay-dependent system with initial condition (w0,q0,θ0,z0)=(-1,0,-0.012,0) and δc=-0.3q-30θ+15z, δe=0.1 (stabilization inside cavity). Here, V=87 m/s.

14. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Cavitator and elevator deflection angles as a function of time for the closed-loop system with δc=-0.3q-30θ+15z, δe=0.1 (stabilization inside cavity). Here, V=87 m/s.

15. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Planing force as a function of time for the closed-loop system with δc=-0.3q-30θ+15z, δe=0.1 (stabilization inside cavity). Here, V=87m/s. Note that the value of the (normalized) planing force approaches zero in steady state.

16. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Cylindrical cavity used for planing force

17. Date of download: 10/22/2017
Copyright © ASME. All rights reserved.
From: Stability Analysis and Control of Supercavitating Vehicles With Advection Delay
J. Comput. Nonlinear Dynam. 2012;8(2): doi: /
Figure Legend:
Cavity and vehicle centerlines for the delayed case