Rotating orbits of a parametrically-excited pendulum

Chaos, Solitons and Fractals

Volumn 23, Issue 5, 2005, Pages 1537-1548

  Xu, Xu ^a   Wiercigroch, M ^a   Cartmell, M P ^b  

^a UNIVERSITY OF ABERDEEN   (United Kingdom)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; CHAOS THEORY; MATHEMATICAL MODELS; NATURAL FREQUENCIES; OSCILLATIONS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; POTENTIAL ENERGY; RESONANCE; VELOCITY MEASUREMENT;

MATHIEU EQUATIONS; RESONANCE TONGUESE; ROTATING ORBITS; VIBRATION SYSTEMS;

PENDULUMS;

EID: 9544249382     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(04)00430-8     Document Type: Article

References (15)

1. Hill GW, On the part of the lunar perigee which is a function of the mean motions of the sun and moon. Acta Math 1886;8:1-36.
2. Nayfeh AH. Introduction to perturbation techniques. John Wiley & Sons, Inc.; 1981.
3. Watt D, Cartmell MP. An externally loaded parametric oscillator. J Sound Vib 1994;170(3):339-64.
4. Leven RW, Koch BP. Chaotic behaviour of a parametrically excited damped pendulum. Phys Lett 1981;86A:71-4.
5. Koch BP, Leven RW. Subharmonic and homoclinic bifurcations in a parametrically forced pendulum. Physica D 1985;16:1-13.
6. Clifford MJ, Bishop SR. Approximating the escape zone for the parametrically excited pendulum. J Sound Vib 1994;172(4):572-6.
7. Bishop SR, Clifford MJ. Zones of chaotic behaviour in the parametrically excited pendulum. J Sound Vib 1996; 189(1): 142-7.
8. Clifford MJ, Bishop SR. Rotating periodic orbits of the parametrically excited pendulum. Phys Lett A 1995;201:191-6.
9. Bishop SR, Clifford MJ. The use of manifold tangencies to predict orbits, bifurcations and estimate escape in driven systems. Chaos, Solitons and Fractals 1996;7(10):1537-53.
10. Clifford MJ, Bishop SR. Locating oscillatory orbits of the parametrically-excited pendulum. J Aust Math Soc Series B-Appl Math 1996;37:309-19.
11. Clifford MJ, Bishop SR. Inverted oscillations of a driven pendulum. Proc R Soc Lond Series A 1998;454:2811-7.
12. Sudor DJ, Bishop SR. Inverted dynamics of a tilted parametric pendulum. Eur J Mech A-Solids 1999;18:517-26.
13. Szemplińska-Stupnicka W, Tyrkiel E. The oscillation-rotation attractors in the forced pendulum and their peculiar properties. Int J Bifurcation and Chaos 2002;12:159-68.
14. Szemplińska-Stupnicka W, Tyrkiel E. Common features of the onset of the persistent chaos in nonlinear oscillators: a phenomenological approach. Nonlinear Dyn 2002;27:271-93.
15. Nusse HE, Yorke AY. Dynamics numerical explorations. New York: Springer-Verlag, Inc.; 1997.