Ponytail motion

SIAM Journal on Applied Mathematics

Volumn 70, Issue 7, 2010, Pages 2667-2672

  Keller, Joseph B ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Hill's equation; Instability; Parametric resonance

Indexed keywords

ANGULAR DISPLACEMENT; FREQUENCY OF OSCILLATION; HILL'S EQUATION; INSTABILITY; LATERAL OSCILLATIONS; PARAMETRIC RESONANCE; RIGID PENDULUMS; VERTICAL MOTIONS;

PARAMETRIC DEVICES; RESONANCE;

PENDULUMS;

EID: 77956233036     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/090760477     Document Type: Article

References (8)

1. J.J.Stoker, Nonlinear Vibrations, Interscience, New York, 1950.
2. W.Magnus and S.Winkler, Hill's Equation, Interscience, New York, 1966.
3. A.Belmonte, M.J.Shelley, S.T.Eldakar, and C.H.Wiggins, Dynamic patterns and self-knotting of a driven hanging chain, Phys.Rev.Lett., 87 (2001), pp.114301-114304.
4. A.Stephenson, On a new type of dynamical stability, Mem.Proc.Manch.Lit. Phil.Soc., 52 (1908), pp.1-10.
5. D.J.Acheson, A pendulum theorem, Proc.Roy.Soc.London Ser.A, 443 (1993), pp.239-245.
6. D.J.Acheson and T.Mullin, Upside-down pendulums, Nature, 366 (1993), pp.215-216.
7. G.H.Handelman and J.B.Keller, Small vibrations of a slightly stiff pendulum, in Proceedings of the 4th U.S.National Congress on Applied Mechanics, Amer.Soc.Mech.Eng., New York, 1963, pp.195-202.
8. A.R.Champneys and W.B.Fraser, The "Indian rope trick" for a parametrically excited flexible rod: Linearized analysis, R.Soc.Lond.Proc.Ser.A Math.Phys.Eng.Sci., 456 (2000), pp.553-570.