1. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Structure of Powerball®

2. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Frames and angles used in the modeling of Powerball®

3. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Phase plane ϕ,ϕ˙: (a) case of Eq. (8) and (b) case of averaged equation, Eq. (12)

4. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Experimental and numerical results of time period Tω of the damped free vibration around the equilibrium point ϕ01

5. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Energy distribution in the phase space

6. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Energy curve in the phase space with φ˙=0

7. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Orbits of phase space and their investigation using separatrix: (a) separatrix obtained from Eq. (18) and several energy curves obtained from Eq. (16) and (b) separatrix obtained from Eq. (18) and orbits from three initial conditions obtained from Eq. (12) (see color figure online)

8. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Entrainment region of synchronous motion (see color figure online)

9. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Experimental system

10. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Experimental result: relation between the initial spin angular velocity γ˙0 and the types of realized motions. Initial precession angle α0 was randomly set: (a) case with initial condition of Θ = 30 deg and Ω = 1.3 Hz and (b) case with initial condition of Θ = 25 deg and Ω = 1.5 Hz.

11. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Experimental result: relation between the initial precession angle α0 and the types of realized motions: (a) case with initial condition of Θ = 25 deg, Ω = 1.5 Hz, and γ˙0 = 2300 rpm (γ˙sync = 2354 rpm) and (b) case with initial condition of Θ = 20 deg, Ω = 1.3 Hz, and γ˙0 = 2000 rpm (γ˙sync = 2040 rpm)

12. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Relationship between the basin of attraction and polar moment of inertia I1: (a) influence of polar moment of inertia I1 on the area J of basin of attraction and (b) basin of attraction of synchronous motion and subsynchronous motion for I1 = 60 μ kg m2 (input parameters: Θ  = 20 deg and Ω  = 1.3 Hz) (see color figure online)

13. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Relationship between the basin of attraction and rotor shaft length Rt: (a) influence of rotor shaft length Rt on the area J of basin of attraction and (b) basin of attraction of synchronous motion and subsynchronous motion for Rt  = 25 mm (input parameters: Θ  = 20 deg and Ω  = 1.3 Hz)

14. From: Nonlinear Dynamical Analysis of the “Power Ball”
Date of download: 10/10/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Dynamical Analysis of the “Power Ball”
J. Comput. Nonlinear Dynam. 2017;12(5): doi: /
Figure Legend:
Influence of rotor shaft radius Ra on the area J of basin of attraction