On the torus flow Y' = A + B cos Y + C cos X and its relation to the quasiperiodic mathieu equation

Proceedings of the ASME Design Engineering Technical Conference

Volumn 7B-1999, Issue , 1999, Pages 1649-1657

  Mason, Stephanie ^a   Rand, Richard ^a  

^a Department of Molecular Biology and Genetics   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

VIBRATIONS (MECHANICAL);

NUMERICAL INTEGRATIONS; PERTURBATION RESULTS; POWER SERIES SOLUTIONS; QUASI-PERIODIC MATHIEU EQUATION;

NUMERICAL METHODS;

EID: 33846118274     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC99-VIB-8052     Document Type: Conference Paper

References (10)

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2. Arnold, V.I. and Avez, A., Ergodic Porblems of Classical Mechanics, Benjamin, New York, 1968.
3. Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
4. Rand, R. and Hastings, R., "A Quasiperiodic Mathieu Equation", Proceedings of the 1995 Design Engineering Technical Conferences, Boston, Massachusetts. Sept. 17-20, 1995, Vol. 3, Part A: Vibration of Nonlinear. Random and Time-Varying Systems, vol. DE-Vol. 84-1, pp. 747-758, American Soc. Mech. Engineers, 1995.
5. Rand, R., Zounes, R., and Hastings, R. "A. Quasiperiodic Mathieu Equation", Nonlinear Dynamics: The Richard Rand 50th Anniversary Volume, Series on Stability, Vibration, and Control of Systems Series B: vol. 2, pp. 203-221, 1997.
6. Rand, R., Zounes, R., and Hastings, R. "Dynamics of a Quasiperiodically-Forced Mathieu Oscillator", IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics, ed. F.C.Moon, Kluwer, Dordrecht, The Netherlands, pp.61-70, 1998.
7. Stoker, J.J., Nonlinear Vibrations in Mechanical and Electrical Systems, Wiley, New York, 1950.
8. Zounes, R. An Analysis of the Nonlinear Quasiperiodic Mathieu Equation, Ph.D. Thesis, Cornell University, Ithaca, NY, 1997.
9. Zounes, R.S. and Rand, R.H., "Transition Curves in the Quasiperiodic Mathieu Equation", in Nonlinear Dynamics and Controls, ed. A.K. Bajaj, N. Sri Na.machchiva.ya, and M.A. Franchek, ASME Book No. G01025, pp.1-6, American Soc. Mech. Engineers, 1996.
10. Zounes, R.S. and Rand, R.H. "Transition Curves for the Quasi-Periodic Mathieu Equation", SIAM J. Appl. Math., vol. 58, no. 4, pp. 1094-1115, August 1998.