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Classical and fractional modelling of oscillatory motion

By Jaromír Hošek

Abstract

In this thesis we deal with the issue of damped oscillations. Besides the classic description using member directly proportional to the first derivative position we focus on the model containing derivatives of non-integer order, so-called the fractional model of damped oscillations. The behavior of both models is studied through the test applications describing the movement of one, two, respectively three bodies connected by springs. The main tool for solving is the Laplace transform method. Besides the computational aspects we discuss some qualitative properties of solutions, especially dependence on order derivative in the fractional model and the behavior of the center of gravity system position

Topics: Differential equation; fractional calculus; Diferenciální rovnice; tlumené kmitání; Laplaceova transformace; Laplace transform; zlomkový kalkulus; damped oscillation
Publisher: Vysoké učení technické v Brně. Fakulta strojního inženýrství
Year: 2013
OAI identifier: oai:invenio.nusl.cz:213911
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