Main chains and eigen modes of fractional order hybrid multipendulum system dynamics

Abstract

A short review of the author's research results in the area of the dynamics of pendulum hybrid systems, as well as an analytical approach to the discrete material particle system dynamics containing creep elements with the constitutive stress-strain relation described by the fractional order derivative are presented. The first results presented in this paper are analytical expressions of the modes of three pendulum fractional order system vibrations. It is shown that two time modes (partial solutions) are pure periodical, and four time modes (particular solutions) are 'creeping modes' as a result of the creeping properties influencing standard light elements to the periodical pendulum mode vibrations with corresponding frequencies. By using an analytical approach, for a fractional order hybrid multipendulum system dynamics, eigen main chains, eigen modes and main coordinates are obtained. The second and generalized result concerns the fractional order hybrid multipendulum system dynamics. © 2009 The Royal Swedish Academy of Sciences.