Vibro-impact dynamics in systems with trigger of couped three singular points

Abstract eng:
Under the author’s use Petroviċ’s elements of mathematical phenomenology, especially mathematical analogy, new expressions of post-collision outgoing angular velocities of two rolling rigid bodies are determined. Advances to theory of collision between two bodies are generalized to collision of two rolling rigid bodies. Using these results, nonlinear dynamics in the vbro-impact system with trigger of coupled singular points and homoclinic trajectory in phase trajectory portraits is study. Use phase portraits of two nonlinear dynamical systems in which appear central collision of thin rolling different size disks are studied. In first vibro-impact system disks is in rolling along straight line and coupled by springs, and in second rolling disks are moving along a circle line rotate with constant angular velocity around vertical central axis. In both considers system dynamics exist a trigger of coupled singular points.

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