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Periodic motions generated from non-autonomous grazing dynamics
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Date
2017-08-01
Author
Akhmet, Marat
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This paper examines impulsive non-autonomous systems with grazing periodic solutions. Surfaces of discontinuity and impact functions of the systems are not depending on the time variable. That is, we can say that the impact conditions are stationary, and this makes necessity to study the problem in a new way. The models play exceptionally important role in mechanics and electronics. A concise review on the sufficient conditions for the new type of linearization is presented. The existence and stability of periodic solutions are considered under the circumstance of the regular perturbation. To visualize the theoretical results, mechanical examples are presented.
Subject Keywords
Non-autonomous impulsive systems
,
Grazing periodic solutions
,
Regular perturbations
,
Impact mechanisms
URI
https://hdl.handle.net/11511/38448
Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
DOI
https://doi.org/10.1016/j.cnsns.2017.02.002
Collections
Department of Mathematics, Article
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Non-autonomous grazing phenomenon
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Non-autonomous grazing phenomenon is investigated through periodic systems and their solutions. The analysis is different than for autonomous systems in many aspects. Conditions for the existence of a linearization have been found. Stability of a periodic solution and its persistence under regular perturbations are investigated. Through examples, the theoretical results are visualized.
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M. Akhmet, “Periodic motions generated from non-autonomous grazing dynamics,”
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
, pp. 48–62, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38448.