Coexisting Periodic Orbits in Vibro-Impacting Dynamical Systems
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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,获得了稳定性的判别式。还以数值模拟结果验证了理论分析的结论。Abstract: Abstract: 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.
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Key words:
- vibro-impact system /
- periodic orbit /
- existence /
- stability
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