In this paper, the analysis of the time evolution of a levitated droplet is proposed. The analysis is composed of two parts: in the first part, a nonlinear dynamics approach was considered to calculate quantities characterizing time series data such as attractor dimension or largest Lyapunov exponent. The number of degrees of freedom in the system was also assessed. Based on the results obtained in the first part, Floquet theory was applied in the second part of the analysis to investigate the stability of the system. Data acquired from a levitation instrument developed by Space Power Institute at Auburn University was used to perform the analysis. [S0739-3717(00)01903-6]

1.
Mestel
,
A. J.
,
1981
, “
Magnetic levitation of liquid metals
,”
J. Fluid Mech.
,
117
, pp.
27
43
.
2.
Busse
,
F. H.
,
1984
, “
Oscillations of a rotating liquid drop
,”
J. Fluid Mech.
,
142
, pp.
1
8
.
3.
Cummings
,
D. L.
, and
Blackburn
,
D. A.
,
1989
, “
Oscillations of magnetically levitated aspherical droplets
,”
J. Fluid Mech.
,
224
, pp.
395
416
.
4.
Chen, S.-F., and Overfelt, A., 1997, “Effects of Sample Size on Surface Tension Measurements of Nickel in Reduced Gravity Parabolic Flight,” in 13th Symposium on Thermophysical Properties, June 22–27, Boulder, CO.
5.
Cusumano
,
J. P.
, and
Moon
,
F. C.
,
1995
, “
Chaotic Non-Planar Vibrations of the Thin Elastica, Part I: Experimental Observation of Planar Instability
,”
J. Sound Vib.
,
179
, No.
2
, pp.
185
208
.
6.
Kang
,
Y.
,
Chang
,
Y. P.
, and
Jen
,
S. C.
,
1998
, “
Strongly Non-Linear Oscillations of Winding Machines, Part I: Mode-Locking Motion and Routes to Chaos
,”
J. Sound Vib.
,
209
, No.
3
, pp.
473
492
.
7.
Nayfeh, A. H., and Balachandran, B., 1995, Applied Nonlinear Dynamics, Wiley, New York.
8.
Farmer
,
J. D.
,
Ott
,
E.
, and
Yorke
,
J. A.
,
1983
, “
The dimension of chaotic attractors
,”
Physica D
,
7
, pp.
153
180
.
9.
Abarbanel, H. D. I., 1996, Analysis of Observed Chaotic Data, Springer-Verlag, New York.
10.
Packard
,
N. H.
,
Crutchfield
,
J. P.
,
Farmer
,
J. D.
, and
Shaw
,
R. S.
,
1980
, “
Geometry from a time series
,”
Phys. Rev. Lett.
,
45
, pp.
712
716
.
11.
Albano
,
A. M.
,
Muench
,
J.
,
Schwartz
,
C.
,
Mees
,
A. I.
, and
Rapp
,
P. E.
,
1988
, “
Singular-value decomposition and the Grassberger-Procaccia algorithm
,”
Phys. Rev. A
,
38
, pp.
3017
3034
.
12.
Provanzale
,
A.
,
Smith
,
L. A.
,
Vio
,
R.
, and
Murante
,
G.
,
1992
, “
Distinguishing between low-dimensional dynamics and randomness in measured time series
,”
Physica D
,
58
, pp.
31
49
.
13.
Cambel, A. B., 1993, Applied Chaos Theory, Academic Press, Boston.
14.
Smith
,
L. A.
,
1988
, “
Intrinsic limits on dimensional calculation
,”
Phys. Lett. A
,
133
, No.
6
, pp.
283
288
.
15.
Grassberger
,
P.
, and
Procaccia
,
I.
,
1984
, “
Dimensions and entropies of strange attractors from a fluctuating dynamics approach
,”
Physica D
,
13
, pp.
34
54
.
16.
Mandelbrot, B., 1983, The Fractal Geometry of Nature, Freeman, San Francisco.
17.
Grassberger
,
P.
, and
Procaccia
,
I.
,
1983
, “
Characterization of strange attractors
,”
Phys. Rev. Lett.
,
50
, No.
5
, pp.
346
349
.
18.
Wolf
,
A.
,
Swift
,
J. B.
,
Swinney
,
H. L.
, and
Vastano
,
J. A.
,
1985
, “
Determining Lyapunov exponents from a time series
,”
Physica D
,
16
, pp.
285
317
.
19.
Eckermann
,
J. P.
,
Kamphorst
,
S. O.
,
Ruelle
,
D.
, and
Ciliberto
,
S.
,
1986
, “
Lyapunov exponents from time series
,”
Phys. Rev. A
,
34
, No.
6
, pp.
4971
4979
.
20.
Kapitaniak, T., 1991, Chaotic Oscillations in Mechanical Systems, Manchaster University Press, New York.
21.
Moon, F. C., 1992, Chaotic and Fractal Dynamics, Wiley, New York.
22.
Theiler
,
J.
,
1991
, “
Some comments on the correlation dimension of 1/fα noise
,”
Phys. Lett. A
,
155
, Nos.
8–9
, pp.
480
493
.
23.
Theiler
,
J.
,
Eubank
,
S.
,
Longtin
,
A.
, and
Galdrikian
,
B.
,
1992
, “
Testing for nonlinearity in time series: The method of surrogate data
,”
Physica D
,
58
, pp.
77
94
.
24.
Chennaoui
,
A.
,
Pawelzik
,
K.
,
Liebert
,
W.
,
Schuster
,
H. G.
, and
Pfister
,
G.
,
1990
, “
Attractor reconstruction from filtered chaotic time series
,”
Phys. Rev. A
,
41
, No.
8
, pp.
4151
4159
.
25.
Agguirre
,
L. A.
,
Mendes
,
E. M.
, and
Billings
,
S. A.
,
1996
, “
Smoothing data with local instabilities for the identification of chaotic systems
,”
Int. J. Control
,
63
, No.
3
, pp.
483
505
.
26.
Broomhead
,
D. S.
, and
King
,
G. P.
,
1986
, “
Extracting qualitative dynamics from experimental data
,”
Physica D
,
20
, pp.
217
236
.
27.
Vautard
,
R.
, and
Ghil
,
M.
,
1989
, “
Singular spectrum analysis in nonlinear dynamics with applications to paleoclimatic time series
,”
Physica D
,
35
, pp.
395
424
.
28.
Casdagli
,
M.
,
1989
, “
Nonlinear prediction of chaotic time series
,”
Physica D
,
35
, pp.
335
356
.
29.
Abarbanel
,
D. I.
,
Frison
,
T. W.
, and
Tsimring
,
L. S.
,
1998
, “
Obtaining order in a world of chaos
,”
IEEE Signal Proc. Mag.
,
15
, No.
3
, pp.
49
65
.
30.
Marghitu
,
D. B.
,
1997
, “
Quantitative Measure of Vehicle Stability
,”
Comput. Model. Simul. Eng.
,
2
, No.
2
, pp.
163
176
.
You do not currently have access to this content.