CODIMENSION TWO BIFURCATIONS AND HOPF BIFURCATIONS OF AN IMPACTING VIBRATING SYSTEM  

作　　者：谢建华 

出　　处：《Applied Mathematics and Mechanics(English Edition)》1996年第1期65-75,共11页应用数学和力学（英文版）

摘　　要：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.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.

关 键 词：impacting vibration STABILITY codimension two bifurcation 

分 类 号：O32[理学—一般力学与力学基础]