The 'Indian rope trick' for a parametrically excited flexible rod: Linearized analysis

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 456, Issue 1995, 2000, Pages 553-570

  Champneys, Alan R ^a   Barrie Fraser, W ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Asymptotic analysis; Floquet theory; Inverted pendulum; Parametric excitation; Rod mechanics

Indexed keywords

EID: 0041676596     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2000.0530     Document Type: Article

References (18)

1. Acheson, D. 1993 A pendulum theorem. Proc. R. Soc. Lond. A 443, 239-245.
2. Acheson, D. 1995 Multiple-nodding oscillations of a driven inverted pendulum. Proc. R. Soc. Lond. A 448, 89-95.
3. Acheson, D. 1997 From calculus to chaos: an introduction to dynamics. Oxford University Press.
4. Acheson, D. & Mullin, T. 1993 Upside-down pendulums. Nature 366, 215-216.
5. Antman, S. S. 1995 Nonlinear problems of elasticity. Applied Mathematical Sciences 107. Springer.
6. Broer, H. & Vegter, G. 1992 Bifurcation aspects of parametric resonance. Dynam. Rep. 1, 1-53.
7. Broer, H., Hoveijn, I. & van Noort, M. 1998 A reversible bifurcation analysis of the inverted pendulum. Physica D112, 50-63.
8. Doedel, E., Champneys, A., Fairgrieve, T., Kuznetsov, Y., Sandstede, B. & Wang, X. 1997 AUTO97 continuation and bifurcation software for ordinary differential equations. Available by anonymous ftp from ftp.cs.concordia.ca, directory pub/doedel/auto.
9. Eraser, W. & Stump, D. 1998 Yarn twist in the ring-spinning balloon. Proc. R. Soc. Lond. A 454, 707-723.
10. Greenhill, A. G. 1881 Determination of the greatest height consistent with stability that a pole or mast can be made, and of the greatest height to which a tree of given proportions can grow. Proc. Camb. Phil. Soc. IV, 65-73.
11. Hunt, G. & Everal, P. 1999 Arnold tongues and mode-jumping in the supercritical post-buckling of an archetypal elastic structure. Proc. R. Soc. Lond. A 455, 125-140.
12. Hurst, C. 1996 The Indian rope trick explained. Aust. Math. Soc. Gazette 23, 154-159.
13. Jordan, D. W. & Smith, P. 1986 Nonlinear ordinary differential equations, 2nd edn. Oxford University Press.
14. Kevorkian, J. & Cole, J. 1981 Perturbation methods in applied mathematics. Springer.
15. Love, A. 1927 A treatise on the mathematical theory of elasticity, 4th edn. Cambridge University Press.
16. Otterbein, S. 1982 Stabilisierung des n-pendels und der indische seiltrick. Arch. Ration. Mech. Analysis 78, 381-393.
17. Stephenson, A. 1908 On a new type of dynamical stability. Mem. Proc. Manch. Lit. Phil. Soc. 52, 1-10.
18. Timoshenko, S. & Gere, J. 1961 Theory of elastic stability, 2nd edn. New York: McGraw-Hill.