Bifurcations of Parametrically Excited Gyroscopic Systems Near a 0 : 1 Resonance
McDonald, Robert Joseph
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https://hdl.handle.net/2142/85134
Description
Title
Bifurcations of Parametrically Excited Gyroscopic Systems Near a 0 : 1 Resonance
Author(s)
McDonald, Robert Joseph
Issue Date
2000
Doctoral Committee Chair(s)
Namachchivaya, N. Sri
Department of Study
Aerospace Engineering
Discipline
Aerospace Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Language
eng
Abstract
The final part of this research involves study of the global bifurcations of the two gyroscopic systems. Using recently developed bifurcation methods, we detect the presence of multi-pulse orbits homoclinic to a slow manifold. In certain parameter regions, we can prove that multi-pulse orbits exist which are homoclinic to fixed points on the slow manifold, leading to chaotic dynamics in the system. These multi-pulse orbits provide the mechanism by which energy transfer between modes may occur.
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