Discontinuous dynamics with grazing points

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2016-09-01

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Akhmet, Marat

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Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of solutions are thoroughly analyzed. A variational system around a grazing solution which depends on near solutions is constructed. Orbital stability of grazing cycles is examined by linearization. Small parameter method is extended for analysis of grazing orbits, and bifurcation of cycles is observed in an example. Linearization around an equilibrium grazing point is discussed. The results can be extended on functional differential equations, partial differential equations and others. Appropriate illustrations are depicted to support the theoretical results.

Subject Keywords

Discontinuous dynamical systems, Grazing points and orbits, Axial and non-axial grazing, Variational system, Orbital stability, Small parameter, Bifurcation of cycles, Impact mechanisms

URI

https://hdl.handle.net/11511/49085

Journal

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

DOI

https://doi.org/10.1016/j.cnsns.2016.02.026

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet, “Discontinuous dynamics with grazing points,” COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, pp. 218–242, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49085.