Abstract
An oscillator which impacts against a rigid barrier is taken into account. A cycle with zero impact velocity is discussed. The main result of this article concerns stability of the grazing cycle. A significant attention to a model with the variable coefficient of restitution depending on velocity is paid. The mechanical reasons for that are provided as well as new theo- retical advantages have been discovered for the investigation of dynamics near a grazing cycle. The W-map which reduces the system with variable moments of impacts to that with fixed moments and simplifies the analy- sis, is defined. A new type of linearization system with two compounds is applied to investigate the stability of the grazing cycle whose existence is easily examined. A new approach to suppress a singularity, caused by the tangency, in linearization has been developed. Simulations are provided to visualize the stability of the grazing cycle.
Original language | English |
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Journal | Discontinuity, Nonlinearity, and Complexity |
Volume | 6 |
Issue number | 2 |
Pages (from-to) | 105-111 |
Number of pages | 7 |
ISSN | 2164-6376 |
DOIs | |
Publication status | Published - 1 Jan 2017 |
Externally published | Yes |
Keywords
- Asymptotic stability
- Grazing periodic solution
- Grazing point
- Linearization at a grazing point
- Variable coefficient of restitution