On the Selection and Meaning of Variable Order Operators for Dynamic Modeling
Joint Authors
Coimbra, Carlos F. M.
Ramirez, Lynnette E. S.
Source
International Journal of Differential Equations
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-12-28
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
We review the application of differential operators of noninteger order to the modeling of dynamic systems.
We compare all the definitions of Variable Order (VO) operators recently proposed in literature and select the VO operator that has the desirable property of continuous transition between integer and non-integer order derivatives.
We use the selected VO operator to connect the meaning of functional order to the dynamic properties of a viscoelastic oscillator.
We conclude that the order of differentiation of a single VO operator that represents the dynamics of a viscoelastic oscillator in stationary motion is a normalized phase shift.
The normalization constant is found by taking the difference between the order of the inertial term (2) and the order of the spring term (0) and dividing this difference by the angular phase shift between acceleration and position in radians (π), so that the normalization constant is simply 2/π.
American Psychological Association (APA)
Ramirez, Lynnette E. S.& Coimbra, Carlos F. M.. 2009. On the Selection and Meaning of Variable Order Operators for Dynamic Modeling. International Journal of Differential Equations،Vol. 2010, no. 2010, pp.1-16.
https://search.emarefa.net/detail/BIM-502861
Modern Language Association (MLA)
Ramirez, Lynnette E. S.& Coimbra, Carlos F. M.. On the Selection and Meaning of Variable Order Operators for Dynamic Modeling. International Journal of Differential Equations No. 2010 (2010), pp.1-16.
https://search.emarefa.net/detail/BIM-502861
American Medical Association (AMA)
Ramirez, Lynnette E. S.& Coimbra, Carlos F. M.. On the Selection and Meaning of Variable Order Operators for Dynamic Modeling. International Journal of Differential Equations. 2009. Vol. 2010, no. 2010, pp.1-16.
https://search.emarefa.net/detail/BIM-502861
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-502861