Proceedings of the Korean Society for Noise and Vibration Engineering Conference (한국소음진동공학회:학술대회논문집)
- 1993.10a
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- Pages.77-83
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- 1993
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- 1598-2548(pISSN)
On the Subharmonic Melnikov Analysis and Chaotic Behaviors in a 2-DOF Hamiltonian System
2자유도 Hamiltonian계의 Subharmonic Melnikov 해석과 혼돈양상에 대한 연구
Abstract
In this paper, the dynamics of a 2-DOF not 1:1 resonant Hamiltonian system are studied. In the first part of the work, the behaviors of special periodic orbits called normal modes are examined by means of the harmonic balance method and their approximate stability ar analyzed by using the Synge's concept named stability in the kinematico-statical sense. Secondly, the global dynamics of the system for low and high energy are studied in terms of a perturbation analysis and Poincare' maps. In this part, one can see that the unstable normal mode generates chaotic motions resulting from the transverse intersections of the stable and unstable manifolds. Although there exist analytic methods for proving the existence of infinitely many periodic orbits, chaos, they cannot be applied in our case and thus, the Poincare' maps constructed by direct numerical integrations are utilized fot detecting chaotic motions. In the last part of the work, the existence of arbitrarily many periodic orbits of the system are proved by using a subharmonic Melnikov's method. We also study the possibility of the breakdown of invariant KAM tori only when h>h
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