A Procedure for Reducing the Chaotic Response Region in an Impact Mechanical System

Nonlinear Dynamics

Volumn 15, Issue 4, 1998, Pages 391-409

  Lenci, Stefano ^a   Rega, Giuseppe ^b  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Chaotic response; Control; Impact; Mechanical systems

Indexed keywords

CHAOS THEORY; CONTROL; NUMERICAL METHODS;

CHAOS CONTROL; CHAOTIC RESPONSE; IMPACT; MECHANICAL SYSTEM;

DYNAMICS;

EID: 0032045936     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008209513877     Document Type: Article

References (15)

1. Bergé, P., Pomeau Y., and Vidal, C., Order Within Chaos, Wiley and Hermann, Paris, 1984.
2. Blazejczyk, B., Kapitaniak, T., Wojewoda, J., and Brindley, J., 'Controlling chaos in mechanical systems', Applied Mechanical Review 46(7), 1993, 385-391.
3. Chen, G. and Dong, X., 'From chaos to order - Perspectives and methodologies in controlling chaotic nonlinear dynamical systems', International Journal of Bifurcation and Chaos 3(6), 1993, 1363-1409.
4. Davis, H. F., Fourier Series and Orthogonal Functions, Allyn and Bacon, Boston, 1963.
5. Ghizzetti, A., 'On the Fourier coefficients of a bounded function, comprised between given limits, Annali Scuola Normale Superiore di Pisa 19, 1950, 131-153 [in Italian].
6. Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields, Springer-Verlag, New York, 1983.
7. Lions, J. L., Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, 1971.
8. Melnikov, V. K., 'On the stability of the center for time periodic perturbations', Transactions of the Moscow Mathematical Society 12, 1963, 1-57.
9. Moore, D. B. and Shaw S. W., 'The experimental response of an impacting pendulum system', International Journal of Non-Linear Mechanics 25, 1990, 1-16.
10. Romeiras, E. J., Grebogi C., Ott, E., and Dayawansa, W. P., 'Controlling chaotic dynamical systems', Physica D 58, 1992, 165-192.
11. Shaw, S. W., 'The suppression of chaos in periodically forced oscillators', in Nonlinear Dynamics in Engineering Systems, Proceedings of IUTAM Symposium, Stuttgart, Germany, August 21-25, 1989, W. Schiehlen (ed.), Springer-Verlag, Berlin, 1990, pp. 289-296.
12. Shaw, S. W. and Rand R. H., 'The transition to chaos in a simple mechanical system', International Journal of Non-Linear Mechanics 24, 1989, 41-56.
13. Wang, H. and Abed, E. H., 'Bifurcation control of chaotic dynamical systems', in Proceedings of 2nd IFAC Nonlinear Control System Design Symposium, Bordeaux, France, June, 1992, pp. 57-62.
14. Wiggins, S., Global Bifurcation and Chaos - Analytical Methods, Springer-Verlag, New York, 1988.
15. Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, 1990.