On the Possibility of the Jerk Derivative in Electrical Circuits
Joint Authors
Aguilar, José Francisco Gómez
Olivares Peregrino, Víctor Hugo
Rosales-García, J.
Escobar-Jiménez, R. F.
López-López, M. G.
Alvarado-Martínez, V. M.
Source
Advances in Mathematical Physics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-11-09
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
A subclass of dynamical systems with a time rate of change of acceleration are called Newtonian jerky dynamics.
Some mechanical and acoustic systems can be interpreted as jerky dynamics.
In this paper we show that the jerk dynamics are naturally obtained for electrical circuits using the fractional calculus approach with order γ .
We consider fractional LC and RL electrical circuits with 1 ⩽ γ < 2 for different source terms.
The LC circuit has a frequency ω dependent on the order of the fractional differential equation γ , since it is defined as ω ( γ ) = ω 0 γ γ 1 - γ , where ω 0 is the fundamental frequency.
For γ = 3 / 2 , the system is described by a third-order differential equation with frequency ω ~ ω 0 3 / 2 , and assuming γ = 2 the dynamics are described by a fourth differential equation for jerk dynamics with frequency ω ~ ω 0 2 .
American Psychological Association (APA)
Aguilar, José Francisco Gómez& Rosales-García, J.& Escobar-Jiménez, R. F.& López-López, M. G.& Alvarado-Martínez, V. M.& Olivares Peregrino, Víctor Hugo. 2016. On the Possibility of the Jerk Derivative in Electrical Circuits. Advances in Mathematical Physics،Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1095962
Modern Language Association (MLA)
Aguilar, José Francisco Gómez…[et al.]. On the Possibility of the Jerk Derivative in Electrical Circuits. Advances in Mathematical Physics No. 2016 (2016), pp.1-8.
https://search.emarefa.net/detail/BIM-1095962
American Medical Association (AMA)
Aguilar, José Francisco Gómez& Rosales-García, J.& Escobar-Jiménez, R. F.& López-López, M. G.& Alvarado-Martínez, V. M.& Olivares Peregrino, Víctor Hugo. On the Possibility of the Jerk Derivative in Electrical Circuits. Advances in Mathematical Physics. 2016. Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1095962
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095962