On the Averaging of Discontinuous Systems

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