Bifurcations and chaotic motions in a rate gyro with a sinusoidal velocity about the spin axis

Journal of Sound and Vibration

Volumn 200, Issue 2, 1997, Pages 121-137

  Ge, Z M ^a   Chen, H H ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012858344     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1996.0695     Document Type: Article

References (20)

1. A. H. NAYFEH and D. T. MOOK 1979 Nonlinear Oscillations. New York: John Wiley. See Chapters 4 and 5.
2. W. SZEMPLIŃSKA-STUPNICKA, R. H. PLAUT and J.-C. HSIEH 1989 Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics 56, 947-952. Period doubling and chaos in unsymmetric structures under parametric excitation.
3. S. N. SINGH 1984 IEEE Transactions on Aerospace and Electronic Systems AES-20, 119-127. Gyro motion boundedness under uncertain vehicle spin and acceleration.
4. Z. M. GE and C. J. CHEN 1992 AIAA Journal of Guidance, Control, and Dynamics 15, 1034-1036. Stability of a rate gyro.
5. J. GUCKENHEIMER and P. HOLMES 1986 Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields. New York; Springer-Verlag. See Chapters 4-7.
6. A. H. MACDONALD and M. PLISCHKE 1983 Physical Review B 27, 201-211. Study of the driven damped pendulum: application to Josephson junctions and charge-density - wave systems.
7. R. RÄTY, J. VON BOEHM and H. M. ISOMÄKI 1984 Physics Letters 103A, 289-292. Absence of inversion-symmetric limit cycles of even periods and the chaotic motion of Duffing's oscillator.
8. J. A. SANDERS and F. VERHULST 1985 Averaging Methods in Nonlinear Dynamics. New York: Springer-Verlag. See Chapter 3.
9. K. YAGASAKI, M. SAKATA and K. KIMURA 1990 Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics 57, 209-217. Dynamics of a weakly nonlinear system subjected to combined parametric and external excitation.
10. N. E. SANCHEZ and A. H. NAYFEH 1990 International Journal of Non-linear Mechanics 25, 163-176. Prediction of bifurcations in a parametrically excited Duffing oscillator.
11. W. SZEMPLIŃSKA-STUPNICKA 1987 Journal of Sound and Vibration 113, 155-172. Secondary resonances and approximate models of routes to chaotic motions in non-linear oscillations.
12. F. H. LING and X. X. WU 1987 International Journal of Non-linear Mechanics 22, 89-98. Fast Galerkin method and its application to determine periodic solution of non-linear oscillators.
13. S. L. LAU, Y. K. CHEUNG and S. Y. WU 1982 Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics 49, 849-853. A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems.
14. Y. K. CHEUNG, S. H. CHEN and S. L. LAU 1990 Journal of Sound and Vibration 140, 273-286. Application of the incremental harmonic balance method to cubic non-linearity systems.
15. L. LAU and S. W. YUEN 1991 Computer Methods in Applied Mechanics and Engineering 91, 1109-1121. The Hopf bifurcation and limit cycle by the incremental harmonic balance method.
16. S. L. LAU and S. W. YUEN 1993 Journal of Sound and Vibration 167, 303-316. Solution diagram of non-linear dynamic systems by the IHB method.
17. P. FRIEDMANN, C. E. HAMMOND and T. H. WOO 1977 International Journal of Numerical Methods in Engineering 11, 1117-1136. Efficient numerical treatment of periodic systems with application to stability problems.
18. Z. M. GE and S. C. LEE 1997 Journal of Sound and Vibration, 199, 189-206. A modified interpolated cell mapping method.
19. A. WOLF, J. B. SWIFT, H. L. SWINNEY and J. A. VASTANO 1985 Physica 16D, 285-317. Determining Lyapunov exponents from a time series.
20. P. FREDERICKSON, J. L. KAPLAN, E. D. YORKE and J. A. YORKE 1983 Journal of Differential Equations 49, 185-207. The Lyapunov dimension of strange attractors.