Coexisting periodic orbits in vibro-impacting dynamical systems. (English) Zbl 1043.70011

Summary: A method is presented to seek in piecewise-linear vibro-impacting systems for coexisting periodic orbits which may be stable or unstable. 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 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 theoretical analysis.


70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
70K40 Forced motions for nonlinear problems in mechanics
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