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Averaging Methods for Second-Order Differential Equations and Their Application for Impact Systems

Author

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  • Michal Fečkan

    (Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
    Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia)

  • Július Pačuta

    (Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia)

Abstract

In this paper, we discuss the averaging method for periodic systems of second order and the behavior of solutions that intersect a hyperplane. We prove an averaging theorem for impact systems. This allows us to investigate the approximate dynamics of mechanical systems, such as the weakly nonlinear and weakly periodically forced Duffing’s equation of a hard spring with an impact wall, or a weakly nonlinear and weakly periodically forced inverted pendulum with double impacts.

Suggested Citation

  • Michal Fečkan & Július Pačuta, 2020. "Averaging Methods for Second-Order Differential Equations and Their Application for Impact Systems," Mathematics, MDPI, vol. 8(6), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:916-:d:367343
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    References listed on IDEAS

    as
    1. Savin Treanţă, 2020. "Gradient Structures Associated with a Polynomial Differential Equation," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    2. Biagio Ricceri, 2020. "A Class of Equations with Three Solutions," Mathematics, MDPI, vol. 8(4), pages 1-8, April.
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