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The following sections are included:

  • Introduction. Types of Discontinuities in Oscillating Systems. Short Review of the Investigations

  • Averaging of Constant Order Discontinuous Systems

  • Averaging of Variable Order Discontinuous Systems

  • On the Averaging of Discontinuous Systems in the Vicinity of a Strong Nonlinear Resonance

  • Constant Order Discontinuous Averaging in Systems with Quasi-Elastic Collisions

  • Resonant Motions in a Quasi-Elastic Colliding Oscillator Excited by an Inertial Source of Limited Power

    • The problem statement

    • Dimensionless formulation. Small parameters

    • Discontinuous variables transformation. Main resonance

    • First step of the hierarchical averaging. Stationary resonance solution

    • Second step of the hierarchical averaging. Attraction area of the resonant solution

    • Concluding remarks

  • Variable Order Discontinuous Averaging in Systems with Inelastic Collisions

  • Conclusions

  • Concluding Remarks of the Editor of the Book

  • References