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BRIEF NOTES

Chaotic Motion of a Symmetric Gyro Subjected to a Harmonic Base Excitation

[+] Author and Article Information
X. Tong

Lucent Technologies, 480 Red Hill Road, Middletown, NJ 07724

N. Mrad

Structures, Materials, and Propulsion Laboratory, Institute for Aerospace Research, National Research Council Canada, 1500 Montreal Road, Building M-3, Ottawa, Ontario K1A 0R6, Canada

J. Appl. Mech 68(4), 681-684 (Feb 25, 2001) (4 pages) doi:10.1115/1.1379036 History: Received July 22, 1997; Revised February 25, 2001
Copyright © 2001 by ASME
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References

Kozlov,  V. V., 1976, “Splitting of Separatrices in the Perturbed Euler-Poinsot Problem,” Moscow Univ. Math. Mech. Bull., 31, pp. 55–59.
Galgoni,  L., Giogilli,  A., and Strlcyn,  J. M., 1981, “Chaotic Motions and Transition to Stochasticity in the Classical Problem of Heavy Rigid Body With Fixed Point,” Nuovo Cimento, 61, pp. 1–20.
Holmes,  P. J., and Marsden,  J. E., 1983, “Melnikov’s Method and Arnold Diffusion for Hamiltonian Systems on Lie Groups,” Indiana Univ. Math. J., 32, pp. 273–309.
Tong,  X., and Rimrott,  F. P. J., 1993, “Chaotic Attitude Motion of Gyrostat Satellites in a Central Force Field,” Nonlinear Dynamics, 4, pp. 269–291.
Tong,  X., and Tabarrok,  B., 1997, “Bifurcation of Self-Excited Rigid Bodies Subject to Small Perturbation Torques,” AIAA Journal of Guidance, Control and Dynamics, 20, pp. 123–128.
Tong,  X., Tabarrok,  B., and Rimrott,  F. P. J., 1995, “Chaotic Motion of an Asymmetric Gyrostat in the Gravitational Field,” Int. J. Non-Linear Mech., 30, pp. 191–203.
Ge,  Z. M., Chen,  H. K., and Chen,  H. H., 1996, “The Regular and Chaotic Motions of a Symmetric Heavy Gyroscope With Harmonic Excitation,” J. Sound Vib., 198, pp. 131–147.
Goldstein, H., 1980, Classical Mechanics, 2nd Ed., Addison-Wesley, Reading, MA.
Melnikov,  V. K., 1963, “On the Stability of the Center for Time Periodic Perturbations,” Transactions of Moscow Mathematical Society, 12, pp. 1–57.
Guckenheimer, J., and Holmes, P. J., 1985, Nonlinear Oscillators, Dynamical Systems and Bifurcations of Vector Fields, 2nd Ed., Springer-Verlag, New York.
Lichtenberg, A. J., and Liberman, M. A., 1992, Regular and Stochastic Motion, 2nd Ed., Springer-Verlag, New York.

Figures

Grahic Jump Location
A symmetric gyro subjected to a harmonic base excitation
Grahic Jump Location
The phase plane of a symmetric gyro
Grahic Jump Location
(a) The Poincaré map of a symmetric gyro (ε=0.01); (b) the Poincaré map of a symmetric gyro (ε=0.1); (c) the Poincaré map of a symmetric gyro (ε=0.5); (d) the Poincaré map of a symmetric gyro (ε=1.0)
Grahic Jump Location
(a) The Poincaré map of a symmetric gyro (δ=2.0 and ε=1.0); (b) the Poincaré map of a symmetric gyro (δ=5.0 and ε=1.0)

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