DocumentCode :
2945860
Title :
Homoclinic and heteroclinic bifurcations of the motion of rotating pendulum
Author :
Elnaggar, Fathy A. ; Elkobrsy, Galal A.
Author_Institution :
Math. Eng. Dept., Alexandria Univ., Egypt
fYear :
2004
fDate :
2004
Firstpage :
338
Lastpage :
343
Abstract :
The goal of this work is to investigate the nonlinear oscillations of the forced, damped rotating pendulum. When the damping coefficient and the amplitude of the excitation force are zero, the system is autonomous with an explicitly known homoclinic and heteroclinic orbits. The homoclinic and the heteroclinic orbits are calculated. Melnikov functions due to the homoclinic and the heteroclinic orbits are calculated to detect the transverse homoclinic and heteroclinic orbits. Regular and chaotic motions are shown to be possible in the damped case. Numerical methods are used to obtain time history, phase portrait, Laypunov exponents, Poincare´ maps and their fractal dimensions.
Keywords :
Lyapunov methods; Poincare mapping; bifurcation; chaos; damping; fractals; nonlinear systems; oscillators; Laypunov exponents; Melnikov functions; Poincare maps; chaotic behavior; damping coefficient; fractal dimensions; heteroclinic bifurcations; homoclinic bifurcations; nonlinear oscillators; rotating pendulum; Bifurcation; Chaos; Damping; Fractals; History; Motion analysis; Nonlinear equations; Nonlinear systems; Orbital calculations; Orbits;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
System Theory, 2004. Proceedings of the Thirty-Sixth Southeastern Symposium on
ISSN :
0094-2898
Print_ISBN :
0-7803-8281-1
Type :
conf
DOI :
10.1109/SSST.2004.1295676
Filename :
1295676
Link To Document :
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