An explicit equation for the dynamics of a particle conveyed by a propagating wave

Minvydas Ragulskis and Edita Sakyte

Mathematical and Computer Modelling of Dynamical Systems, 2009, vol. 15, issue 4, 395-405

Abstract: An explicit governing equation of motion describing nonlinear dynamics of a particle conveyed by a propagating surface wave is deduced. A dynamic equilibrium is constructed at the contact point of the particle and the surface. The mathematical model of the system is constructed in such a way that it involves dynamically shifted coordinates around the contact point. Such an approach yields an explicit nonlinear differential equation. Coexisting attractors and their basin boundaries can be analysed in the general case. Special computational techniques are developed for numerical integration of such differential equations with dynamically shifted coordinates. Attractor control strategy based on small external impulses is proposed when stable equilibrium points and a limit cycle coexist. Such control strategies can dramatically increase the effectiveness of operation and can be applicable in different areas of engineering where positioning or conveyance is performed by means of propagating surface waves.

Date: 2009
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DOI: 10.1080/13873950903063108

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