摘要
提出一种寻找分段线性碰振系统中的多个周期轨道共存的分析方法,这些单碰周期轨道包含稳定的和不稳定的轨道· 给出了单碰周期轨道存在性或不存在性的解析判别式,特别是对如何保证在单碰周期运动中不会发生其它的碰撞的问题作了比较深入的研究,得到若干定理· 最后讨论了所得共存周期轨道的稳定性问题。
A method is presented to seek for coexisting periodic orbits which may be stable or unstable in piecewise_linear vibro_impacting systems.The conditions for coexistence of single impact periodic orbits are derived,and in particular,it is investigated in details how to assure that no other impacts will happen in an evolution period of a single impact periodic motion.Furthermore,some criteria for nonexistence of single impact periodic orbits with specific periods are also established.Finally,the stability of coexisting periodic orbits is discussed, and the corresponding computation formula is given.Examples of numerical simulation are in good agreement with the theoretic analysis.
出处
《应用数学和力学》
EI
CSCD
北大核心
2003年第3期234-244,共11页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(重大19990510
19872010)
教育部博士学科点基金资助项目(98000619)
