Complexity of Motions of Gyroscope

Hu Zhixing; Guan Keying

Volume 25 Issue 5

May 1999

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Journal of Beijing University of Aeronautics and Astronautics > 1999 > 25(5): 596-600.

Huang Jun, Wu Zhe, Zhu Rongchanget al. Optimized Collocation of Combat Aircraft Weapon Systems for Air Force[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(5): 546-549. (in Chinese)

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Hu Zhixing, Guan Keying. Complexity of Motions of Gyroscope[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(5): 596-600. (in Chinese)

Citation:

Hu Zhixing, Guan Keying. Complexity of Motions of Gyroscope[J]. Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(5): 596-600. (in Chinese)

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Complexity of Motions of Gyroscope

Beijing University of Aeronautics and Astronautics, School of Science

Received Date: 17 Apr 1998
Publish Date: 31 May 1999

Abstract

Abstract

The motions of a gravity symmetric gyroscope, whose outer ring's axis is placed horizontally, are dealt with. Firstly, the motions of a free gyroscope are studied and explained in the sense of mechanics under a certain condition. The Melnikov's methods and KAM theory can be used to study the motions of a non-free gyroscope if its rotor's gravity center can be treated as a perturbation. It is shown that the motions of the non free gyroscope are chaotic in the sense of Smale horseshoe, and the KAM invariant tori and closed curves exist in the Hamiltonian flows of the perturbed system if the gravity center of the gyroscope's rotor doesn't coincide with the center of its supports, and the distance between them is sufficiently small, or its energy is sufficiently large in comparison with its potential energy.
- gyroscopes,
- gravity,
- motion,
- chaos,
- Melnikov function,
- invariant tori,
- KAM theory

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References(1)

References

1. 马格奴斯 K. 陀螺理论与应用. 北京: 国防工业出版社, 1983 2. 刘延柱. 万向支架陀螺仪的摄动理论. 力学与实践, 1982, 4(3):37~39 3. Guan K Y. The KAM theory of double pendulum. Ann of Diff Eqs, 1998, 14(2):120~130 4. 胡志兴,管克英. 复杂双摆的KAM理论. 高校应用数学学报(A),1999,14(2):147~154 5. Guckenheimer J, Holmes P. Nonlinear oscillations, dynamical systems, and bifurcation of vector fields. New York:Springer-Verlag, 1983 6. Arnold V I. Mathematical methods of classical mechanics. Berlin:Springer-Verlag, 1978

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Complexity of Motions of Gyroscope