The damping-induced self-recovery phenomenon is well understood for finite-dimensional mechanical systems. In this paper, we discover a self-recovery phenomenon in a composite system that consists of a cylindrical vessel and a surrounding fluid, where the vessel is equipped with an internal rotor and the fluid is incompressible and viscous. In the system dynamics, interactions between the vessel and the ambient fluid are fully taken into account. A combination of the Lyapunov method and the final-value theorem is applied for analysis of the dynamics. It is mathematically shown that after the spin of the rotor comes to a complete stop in finite time or exponentially as time tends to infinity, the vessel, which has deviated from its initial position due to the reaction to rotor spinning, converges back to its initial position as time tends to infinity, and so does every fluid particle. An experimental test is conducted to verify the occurrence of this phenomenon. The simultaneous self-recovery of the vessel and the fluid to the initial configuration is induced by the fluid viscosity as if the viscosity has a memory of the initial configuration. We envision that our discovery may be useful in designing and operating mechatronic systems interacting with fluids such as underwater vehicles.

References

References
1.
Chang
,
D. E.
, and
Jeon
,
S.
,
2013
, “
Damping-Induced Self Recovery Phenomenon in Mechanical Systems With an Unactuated Cyclic Variable
,”
ASME J. Dyn. Syst., Meas., Control
,
135
(
2
), p.
021011
.10.1115/1.4007556
2.
Chang
,
D. E.
, and
Jeon
,
S.
,
2013
, “
On the Damping-Induced Self-Recovery Phenomenon in Mechanical Systems With Several Unactuated Cyclic Variables
,”
J. Nonlinear Sci.
,
23
(
6
), pp.
1023
1038
.10.1007/s00332-013-9177-2
3.
Chang
,
D. E.
, and
Jeon
,
S.
, “
Video of an Experiment That Demonstrates the Self-Recovery Phenomenon in the Bicycle Wheel and Rotating Stool System
,” http://www.youtube.com/watch?v=og5h4QoqIFs
4.
Chang
,
D. E.
, and
Jeon
,
S.
, “
On the Self-Recovery Phenomenon in the Process of Diffusion
,” preprint arXiv:1305.6658.
5.
Chang
,
D. E.
, and
Jeon
,
S.
, “
Video of an Experiment That Demonstrates the Self-Recovery Phenomenon in the Vessel and Fluid System
,” http://www.youtube.com/watch?v=26qGQccK4Rc
6.
Jacobs
,
H.
,
Ratiu
,
T. S.
, and
Desbrun
,
M.
,
2013
, “
On the Coupling Between an Ideal Fluid and Immersed Particles
,”
Physica D
,
265
, pp.
40
56
.10.1016/j.physd.2013.09.004
7.
Kanso
,
E.
,
Marsden
,
J. E.
,
Rowley
,
C. W.
, and
Melli-Huber
,
J.
,
2005
, “
Locomotion of Articulated Bodies in a Perfect Fluid
,”
J. Nonlinear Sci.
,
15
(4), pp.
255
289
.10.1007/s00332-004-0650-9
8.
Koiller
,
J.
,
Ehlers
,
K.
, and
Montgomery
,
R.
,
1996
, “
Problems and Progress in Microswimming
,”
J. Nonlinear Sci.
,
6
(6), pp.
507
541
.10.1007/BF02434055
9.
Leonard
,
N. E.
, and
Marsden
,
J. E.
,
1997
, “
Stability and Drift of Underwater Vehicle Dynamics: Mechanical Systems With Rigid Motion Symmetry
,”
Physica D
,
105
(
1–3
), pp.
130
162
.10.1016/S0167-2789(97)83390-8
10.
Shashikanth
,
B. N.
,
2006
, “
Symmetric Pairs of Point Vortices Interacting With a Neutrally Buoyant Two-Dimensional Circular Cylinder
,”
Phys. Fluids
,
18
(12), p.
127103
.10.1063/1.2400209
11.
Taylor
,
G.
,
1951
, “
Analysis of the Swimming of Microscopic Organisms
,”
Proc. R. Soc. London A
,
209
(
1099
), pp.
447
461
.10.1098/rspa.1951.0218
12.
Taylor
,
G.
,
1952
, “
Analysis of the Swimming of Long and Narrow Animals
,”
Proc. R. Soc. London A
,
214
(
1117
), pp.
158
183
.10.1098/rspa.1952.0159
13.
Vankerschaver
,
J.
,
Kanso
,
E.
, and
Marsden
,
J. E.
,
2009
, “
The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices
,”
J. Geom. Mech.
,
1
(
2
), pp.
227
270
.10.3934/jgm.2009.1.223
14.
Landau
,
L. D.
, and
Lifshitz
,
E. M.
,
1959
,
Fluid Mechanics
,
Addison-Wesley Publishing Company, Inc.
, Reading, MA.
15.
Abramowitz
,
M.
, and
Stegun
,
I. A.
,
1965
,
Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables
,
Dover Publications
,
New York
.
16.
Maples
,
R. E.
,
2000
,
Petroleum Refinery Process Economics
,
PennWell Books
, Tulsa, OK.
You do not currently have access to this content.