Abstract
Bifurcation problems of a spring-mass system vibrating against an infinite large plane are studied in this paper. It is shown that there exist phenomena of codimension two bifurcations when the ratios of frequencies are in the neigborhood of the same special values and the coefficient of restitution approach unity. By theory of normal forms, we reduce Poincare maps to normal forms, and find flip bifurcations, Hopf bifurcations of fixed points and that of period two points. The theoretical solutions are verified by numerical computations.
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Communicated by Li Li
Project supported by the National Science Foundation of China
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Jianhua, X. Codimension two bifurcations and hopf bifurcations of an impacting vibrating system. Appl Math Mech 17, 65–75 (1996). https://doi.org/10.1007/BF00131296
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DOI: https://doi.org/10.1007/BF00131296