文章基本信息

标题：A Fractional Variational Approach for Modelling Dissipative Mechanical Systems:Continuous and Discrete Settings
本地全文：下载
作者：Fernando Jiménez ; Sina Ober-Blöbaum
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2018
卷号：51
期号：3
页码：50-55
DOI：10.1016/j.ifacol.2018.06.013
语种：English
出版社：Elsevier
摘要：AbstractEmploying a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional Euler-Lagrange equations (both in the continuous and discrete settings), which, as we show, are invariant under linear change of variables. This principle relies on a particular restriction upon the admissible variation of the curves. In the case of the half-derivative and mechanical Lagrangians, i.e. kinetic minus potential energy, the restricted fractional Euler-Lagrange equations model a dissipative system in both directions of time, summing up to a set of equations that is invariant under time reversal. Finally, we show that the discrete equations are a meaningful discretisation of the continuous ones.
关键词：KeywordsVariational analysisMechanical systemsLagrangian mechanicsDampingFractional derivativesDiscretisationVariational integrators