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Existence of Triggers of Coupled Singularities in Nonlinear Dynamics of Mechanical Systems with Coupled Rotations
Katica Stevanović-Hedrih
A theorem of triggers of coupled singularities is presented as well as numerous examples of nonlinear dynamics of mechanical systems with coupled singularities in phase portraits. Abstractions of real engineering system nonlinear dynamics with rotations coupled into the model of a rigid body which performs coupled rotations around nonintersecting axes in the gravitational field shows numerous varieties of the homoclinic phase of trajectories as well as different sets of tigers of coupled singularities. A multi-parameter transformation of the phase trajectories and of the set of coupled singularities is presented. In addition, a series of triggers of coupled singularities in the phase portraits is given as well as the trigger of coupled half-one side singularities identified in the heavy mass particle oscillations/motion along a rotating rough curvilinear line and non-ideal constraints of Amontons-Coulomb friction. An example is used to show the heavy mass particle motion along rough curvilinear lines in the vertical plane, described by a corresponding differential double equation and the double equation of the phase trajectories, while more triggers of coupled half-one side singularities are identified in the phase portrait. Key words: mechanical system, trigger, nonlinear dynamics, coupled singularity, rotating system.
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