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Periodic solutions of measure differential inclusions
Author(s) -
Paschkowski Manuela,
Arnold Martin
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800066
Subject(s) - differential inclusion , measure (data warehouse) , mathematical analysis , mathematics , space (punctuation) , simple (philosophy) , differential (mechanical device) , physics , computer science , thermodynamics , philosophy , epistemology , database , operating system
When modelling mechanical systems with contact and impact forces the most important characteristic is the occurrence of velocity jumps during the impacts. Even for simple applications like the bouncing ball [3] or the impact oscillator [1] this nonsmooth effect may arise infinitely often during a finite time. A suitable setting, whose solution space includes such strongly nonsmooth functions, are the measure differential inclusions (MDI) [7]. The mentioned framework is used to prove existence of periodic solutions for the impact oscillator independent of initial values or system parameters.