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Chaotic motion of a horizontal impact pair. (English) Zbl 1237.70028

Summary: A theory for a system with discontinuities and applied to the impact analysis of a horizontal impact pair is presented. Mappings for four switch-planes are defined and from these several impact models are developed. As a case of special interest, the case of a steady state, periodic two-impacts/\(N\)-cycles motion is studied in greater detail. Numerical simulations of the various models are also given. The results show that the ensuing chaotic behavior can be eitherregularwith period-doubling bifurcation orrandomwith other types of bifurcation. The former refers to chaos, where its mathematical structure is regular, while the latter refers to one with a random mathematical structure.

MSC:

70F35 Collision of rigid or pseudo-rigid bodies
70K50 Bifurcations and instability for nonlinear problems in mechanics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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