Global behavior of a nonlinear quasiperiodic Mathieu equation

Proceedings of the ASME Design Engineering Technical Conference

Volumn 6 C, Issue , 2001, Pages 2495-2505

  Zounes, Randolph S ^a   Rand, Richard H ^a  

^a Cornell University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; HAMILTONIANS; HARMONIC ANALYSIS; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; NATURAL FREQUENCIES; NONLINEAR EQUATIONS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; DESIGN; RESONANCE; VIBRATIONS (MECHANICAL);

ELLIPTIC FUNCTIONS; LIE TRANSFORM; NONLINEAR QUASIPERIODIC MATHIEU EQUATION; SUBHARMONIC RESONANCES; TRIGONOMETRIC FUNCTIONS; ANALYTIC EXPRESSIONS; GLOBAL BEHAVIORS; PERTURBATION THEORY; POINCARE SECTIONS; QUASI-PERIODIC MATHIEU EQUATION; SUB-HARMONIC RESONANCES;

RESONANCE; NONLINEAR EQUATIONS;

EID: 0035791279     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (7)

1. B. V. Chirikov, A universal instability of many-dimensional oscillator systems, Physics Reports, 52 (1979), pp. 263-379.
2. J. Guckenheimer, M. Myers, F. Wicklin, and P. Worfolk, dstool: A Dynamical System Toolkit with an Interactive Graphical Interface, Department of Applied Mathematics, Cornell University, Ithaca, New York, 1991.
3. S. Mason and R. Rand, On the torus flow y′ = a + b cos y + c cos x and its relation to the quasiperiodic Mathieu equation, Proceedings of the 1999 ASME Design Engineering Technical Conferences, 17th Biennial Conference on Mechanical Vibration and Noise, Las Vegas, NV, Sept. 12-15, 1999, Paper no.DETC99/VIB-8052 (CD-ROM).
4. R. Rand, R. Zounes, and R. Hastings, Dynamics of a quasiperiodically forced Mathieu oscillator, Chapter 9 in "Nonlinear Dynamics: The Richard Rand, 50th Anniversary Volume", A. Guran, ed. World Scientific Pub.Co. (1997) pp.203-221.
5. R. Zounes, An analysis of the nonlinear quasiperiodic Mathieu equation, Ph.D. Dissertation, Center for Applied Mathematics, Cornell University, Ithaca, NY, May 1997.
6. R. Zounes and R. Rand, Subharmonic resonance in the nonlinear Mathieu equation, International J. Nonlinear Mechanics. To appear, 2001.
7. ____, Transition curves for the quasiperiodic Mathieu equation, SIAM J. Appl. Math., 58 (1998), pp. 1094-1115.