Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping

Journal of Sound and Vibration

Volumn 255, Issue 4, 2003, Pages 719-740

  Chen, H K ^a  

^a HSIUPING INSTITUTE OF TECHNOLOGY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHAOS THEORY; DAMPING; FEEDBACK CONTROL; PHASE DIAGRAMS; STABILITY; SYNCHRONIZATION;

ADAPTIVE CONTROL ALGORITHMS; CHAOS SYNCHRONIZATION; CHAOTIC MOTION; HARMONIC EXCITATION; LIAPUNOV DIMENSIONS; LIAPUNOV EXPONENTS; LINEAR PLUS CUBIC DAMPING;

GYROSCOPES;

EID: 0037461477     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.2001.4186     Document Type: Article

References (16)

1. R.-B. Leipnik and T.-A. Newton 1981 Physics Letters 86A, 63-67. Double strange attractors in rigid body motion with feedback control.
2. Z.-M. Ge, H.-K. Chen and H.-H. Chen 1996 Journal of Sound and Vibration 198, 131-147. The regular and chaotic motions of a symmetric heavy gyroscope with harmonic excitation.
3. Z.-M. Ge and H.-K. Chen 1996 Japanese Journal of Applied Physics 35, 1954-1965. Stability and chaotic motions of a symmetric heavy gyroscope.
4. X. Tong and N. Mrad 2001 Transactions of American Society of Mechanical Engineers, Journal of Applied Mechanics 68, 681-684. Chaotic motion of a symmetric gyro subjected to a harmonic base excitation.
5. H. Poincaré 1899 Les Methodes Nouvelles De La Mecanique. Paris: Gauthier-Villiars.
6. E.-N. Lorenz 1963 Journal of Atmospheric Science 20, 130-141. Deterministic non-periodic flow.
7. Y. Braiman and I. Goldhirsh 1991 Physical Review Letters 66, 2545-2548. Taming chaotic dynamics with weak periodic perturbations.
8. E. Ott, C. Grebogi and J.-A. Yorke 1990 Physical Review Letters 64, 1196-1199. Controlling chaos.
9. B.-A. Huberman and E. Lumer 1990 IEEE Transactions on Circuits and Systems 37, 547-550. Dynamics of adaptive system.
10. L.-M. Pecora and T. L. Carroll 1990 Physical Review Letters 64, 821-824. Synchronization in chaotic systems.
11. M. Lakshmanan and K. Murali 1996 Chaos in Nonlinear Oscillators: Controlling and Synchronization. Singapore: World Scientific.
12. F.-R. Gantmacher 1960 Lectures on Analytic Mechanics (Gosudarstvennoe Izdat'elstvo Fiziko Mat'emat'iskoi Literaturi, Moscow, 1960) (in Russian).
13. M. Vidyasagar 1993 Nonlinear Systems Analysis. London: Prentice-Hall.
14. L. Cveticanin 1995 Transactions of American Society of Mechanical Engineers, Journal of Applied Mechanics 62, 227-229. A note on the stability and instability of system with time variable parameters.
15. A. Wolf, J.-B. Swift, H.-L. Swinney and J. A. Vastano 1985 Physica 16 D, 285-317. Determining Liapunov exponents from a time series.
16. P. Frederickson, J.-L. Kaplan, E.-D. Yorke and J.-A. Yorke 1983 Journal of Differential Equations 49, 185-207. The Liapunov dimension of strange attractors.