Proceedings of the American Mathematical Society

Author(s): Dingbian Qian
Journal: Proc. Amer. Math. Soc. 133 (2005), 1797-1804.
MSC (2000): Primary 34C15, 34C25, 34B30
Posted: December 20, 2004
Retrieve article in: PDF DVI PostScript

Abstract: A result of A. Lazer and P. McKenna is extended to show the existence of large amplitude periodic bouncing for a damped linear impact oscillator with multiple impacts during one period.

1.: V.I. Babitsky, Theory of vibro-impact systems and applications. Springer-Verlag, 1998. MR 1647097 (99j:70026)
2.: C. Bapat, Periodic motions of an impact oscillator. Journal of Sound and Vibration 209 (1998), 43-60.
3.: D. Bonheure and C. Fabry, Periodic motions in impact oscillators with perfectly elastic bounces. Nonlinearity 15 (2002), 1281-1298. MR 1912295 (2003f:34080)
4.: M. Corbera and J. Llibre, Periodic orbits of a collinear restricted three body problem. Celestial Mech. Dynam. Astronom. 86 (2003), 163-183. MR 1988412 (2004c:70015)
5.: M. Kunze, Non-smooth Dynamical Systems. Lecture Notes in Math. 1744, Springer-Verlag, 2000. MR 1789550 (2002e:34002)
6.: H. Lamba, Chaotic, regular and unbounded behaviour in the elastic impact oscillator. Phys. D 82 (1995), 117-135. MR 1324244 (96m:70032)
7.: A. Lazer and P. McKenna, Periodic bouncing for a forced linear spring with obstacle. Diff. Int. Equs. 5 (1992), 165-172. MR 1141733 (92m:34082)
8.: R. Ortega, Dynamics of a forced oscillator with obstacle. In: Variational and Topological Methods in the Study of Nonlinear Phenomena, edited by V. Benci etal., 77-89, Birkh $\ddot{\hbox{a}}$ user, Boston, 2001. MR 1879730 (2002h:00021)
9.: L. Paoli and M. Schatzman, Resonance in impact problems. Math. Comput. Modelling 28 (1998), 385-406. MR 1648765 (99g:73074)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34C15, 34C25, 34B30

Dingbian Qian
Affiliation: Department of Mathematics, Suzhou University, Suzhou 215006, People's Republic of China
Email: dbqian@suda.edu.cn

DOI: 10.1090/S0002-9939-04-07759-7
PII: S 0002-9939(04)07759-7
Keywords: Impact oscillator with damping, bouncing periodic solution, multiple impacts
Received by editor(s): February 10, 2003
Received by editor(s) in revised form: February 23, 2004
Posted: December 20, 2004
Additional Notes: This work was supported by NNSF of China No.10271085 and NSF of Jiangsu Province, China No.BK2002037, 02KJB110003
Communicated by: Carmen C. Chicone
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS