Premium
Mechanics with variable‐order differential operators
Author(s) -
Coimbra C.F.M.
Publication year - 2003
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200310032
Subject(s) - variable (mathematics) , time scale calculus , differential operator , calculus (dental) , operator (biology) , differential calculus , differential equation , simple (philosophy) , mathematics , differential (mechanical device) , work (physics) , order (exchange) , constant (computer programming) , computer science , mathematical analysis , multivariable calculus , physics , philosophy , dentistry , repressor , chemistry , engineering , biochemistry , epistemology , transcription factor , thermodynamics , programming language , medicine , control engineering , gene , finance , economics
This work presents the novel concept of Variable‐Order (VO) Calculus through the description of a simple problem in Mechanics. A mathematical definition for the VO‐differential operator that is suitable to mechanical modelling is proposed, and an example concerning the effect of nonuniform viscoelastic frictional forces is described. A numerical method for the solution of Variable Order Differential Equations (VODEs) is proposed. The physical model under study requires mathematical tools that lie beyond the traditional methods of Constant‐Order (CO) differential equations. The VO‐Calculus formulation is compared to a CO‐Calculus model in order to show the limitations of the latter in resolving the transition between the relevant dynamic regimes.