Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Meehan, P. A. and Asokanthan, S. F. (2006) Analysis of chaotic instabilities in a rotating body with internal energy dissipation. International Journal of Bifurcation And Chaos, 16 1: 1-19.


Author Meehan, P. A.
Asokanthan, S. F.
Title Analysis of chaotic instabilities in a rotating body with internal energy dissipation
Journal name International Journal of Bifurcation And Chaos   Check publisher's open access policy
ISSN 0218-1274
Publication date 2006
Sub-type Critical review of research, literature review, critical commentary
DOI 10.1142/S021812740601454X
Volume 16
Issue 1
Start page 1
End page 19
Total pages 19
Editor Leon O. Chua
Place of publication Singapore
Publisher World Scientific Publishing Co. Pte. Ltd.
Collection year 2006
Language eng
Subject C1
291899 Interdisciplinary Engineering not elsewhere classified
780102 Physical sciences
Abstract Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.
Keyword Mathematics, Interdisciplinary Applications
Multidisciplinary Sciences
Chaos
Melnikov
Spacecraft
Lyapunov
Bifurcations
Circumferential Nutational Damper
Spinning Spacecraft
Motion
Satellite
Gyrostat
System
Q-Index Code C1

Document type: Journal Article
Sub-type: Critical review of research, literature review, critical commentary
Collections: Excellence in Research Australia (ERA) - Collection
School of Mechanical & Mining Engineering Publications
2007 Higher Education Research Data Collection
 
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Created: Wed, 15 Aug 2007, 07:57:00 EST