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- Title
Averaging Methods for Second-Order Differential Equations and Their Application for Impact Systems.
- Authors
Fečkan, Michal; Pačuta, Július
- 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.
- Subjects
AVERAGING method (Differential equations); DUFFING equations; HAMILTONIAN systems
- Publication
Mathematics (2227-7390), 2020, Vol 8, Issue 6, p916
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math8060916