On the analysis of time-periodic nonlinear Hamiltonian dynamical systems

Proceedings of the ASME Design Engineering Technical Conference

Volumn 3A-1995, Issue , 1995, Pages 375-386

  Butcher, Eric A ^a   Sinha, S C ^a  

^a AUBURN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; DYNAMICAL SYSTEMS; LINEAR TRANSFORMATIONS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR ANALYSIS; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES; TIME VARYING SYSTEMS; VIBRATIONS (MECHANICAL);

ACTION-ANGLE COORDINATES; ALGEBRAIC MANIPULATIONS; ANALYSIS TECHNIQUES; HAMILTONIAN DYNAMICAL SYSTEMS; HAMILTONIAN PERTURBATION THEORY; METHOD OF AVERAGING; NORMAL FORM THEORY; PARAMETRIC EXCITATIONS;

HAMILTONIANS;

EID: 85103460064     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC1995-0277     Document Type: Conference Paper

References (26)

1. Abraham, R. and Marsden, J., 1978, Foundations ofMechanics, Benjamin/Cummings, Reading, MA.
2. Arnold, V. I., 1978, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York.
3. Arnold, V. I., 1983, Geometrical Methods in the Theory of Ordinary Differential Equations. Springer-Verlag, New York.
4. Arrowsmith, D. K., and Place, C. M., 1990, An Introduction to Dynamical Systems, Cambridge University Press, Cambridge.
5. Bemussou, J., 1977, PointMapping Stability. Pergamon Press.
6. Butcher, E. A. and Sinha, S. C., 1995, Transformations of Linear Hamiltonian Systems to Real Normal Forms via Permutation Matrices, submitted to Celestial Mechanics and DynamicalAstronomy.
7. Coddington, E. A., and Levinson, N., 1955, Theory of Ordinary Differential Equations. McGraw Hill, New York.
8. Flashner, H., and Hsu, C. S., A Study of nonlinear periodic systems via the point mapping method. Intern. J. Numer. Meth. Eng., 1983, Vol. 19, pp 185-215.
9. Goldstein, H., 1980, Classical Mechanics, Addison-Wesley, Reading, MA.
10. Horn, R.A. and Johnson, C.R., 1985, Matrix Analysis, Cambridge Univ. Press, New York.
11. Joseph, P., Pandiyan, R., and Sinha, S. C., 1993, Optimal Control ofMechanical Systems Subjected to Periodic Loading via Chebyshev Polynomials. Optimal Control Applications and Methods, Vol. 14, 75-90.
12. Kleczka, M., Kreuzer, E., and Schiehlen, W., 1992, Local and Global Stability of a Piecewise Linear Oscillator, Phil. Trans. R. Soc. Lond. A, 338, pp. 533-546.
13. Liapunov,A.M., 1896, Sur une serie relative a la theorie des equations differentielles lineaires a coefficients periodiques. Compt. Rend. 123, No. 26, pp. 1248 - 1252.
14. Lichtenberg, A. J. and Lieberman, M. A., 1992, Regular and ChaoticDynamics, Springer-Verlag, New York.
15. Lindtner, E., Steindl, A., and Troger, H., 1990, Generic one-parameter bifurcations in the motion of a simple robot, in Continuation Techniques and Bifurcation Problems, Ed. H.D. Mittelmann and D. Roose, pp 199-218.
16. Meyer, K.R. and Hall, G.R., 1992, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Springer-Verlag, New York.
17. Nayfeh,A. H., and Mook, D.T.,1979, Nonlinear Oscillations, Wiley, New York.
18. Pandiyan, R., and Sinha, S. C., 1994, Time-Varying Controller Synthesis for Structures Subjected to Parametric Periodic Loadings, 35th SDM Conference, Part 5, pp. 2449-2459, April 18-20, Hilton head, SC.
19. Pandiyan, R., Butcher, E. A., and Sinha, S. C., 1994, On the Approximation of Dynamical Systems Subjected to Strong Parametric Excitations, in Nonlinear and Stochastic Dynamics, 1994 Winter Annual ASME Meeting proceedings, Nov. 6-11, 1994, Chicago, IL, AMD v. 192, DE v. 78, ed. A.K. Bajaj, N.S. Namachchivaya, and R.A. Ibrahim,
20. Rosenblat, S., and Cohen, D.S., 1980, Periodically perturbed Bifurcation I, Simple Bifurcation. Studies in Applied Mathematics, 63, pp. 1-23.
21. Sanders,J.A., and Verhulst,F., 1985, Averaging Methods in Nonlinear Dynamical Systems, Springer - Verlag, New York.
22. Sinha, S. C., and Wu, D-H., 1991, An Efficient Computational Scheme for the Analysis of Periodic Systems. J. of Sound and Vibration, Vol. 151, pp. 91-117.
23. Sinha, S.C., Wu,D-H., Juneja, V., and Joseph, P., 1993, Analysis of Dynamic Systems With Periodically Varying Parameters via Chebyshev Polynomials. Journal of Vibration and Acoustics, Trans, ofASME, Vol. 115, pp. 96-102.
24. Sinha, S. C., and Pandiyan, R., 1994, Analysis of Quasilinear Dynamical Systems with Periodic Coefficients Via Liapunov-Floquet Transformation, International Journal of Non-Linear Mechanics, Vol, 29, pp. 687-702.
25. Yakubovich V. A., and Starzhinskii V. M., 1975, Linear Differential Equations with Periodic Coefficients, Part I and Part n, John Wiley & Sons, New York.
26. Zaslavsky, G.M., 1985, Chaos in Dynamic Systems, Harwood, New York.