Vibrodynamics studies motions of various dynamical (mechanical, biological, etc.) systems in the presence of the high frequency oscillations of their parameters. Considered systems could be described by either ODEs or PDEs. The lecture exposes the most essential steps used for the deriving of the averaged versions of such equations. Two simple examples will be considered. The first one is the ‘Kapitza pendulum’, known also as the ‘up side down pendulum’ where we expose the averaging procedure for an ODE (the Newton equation). The second examples operate with a PDE; we consider the advection of a scalar field (a simplest hyperbolic equation). The level of presentation is chosen to be ‘as simple as possible’, so the material will be certainly accessible for the graduate students, researchers, and engineers.  

Keywords: Averaging Methods; ODEs, PDEs.

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