On the Possibility of the Jerk Derivative in Electrical Circuits
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...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/9740410 |
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| author | J. F. Gómez-Aguilar J. Rosales-García R. F. Escobar-Jiménez M. G. López-López V. M. Alvarado-Martínez V. H. Olivares-Peregrino |
| author_facet | J. F. Gómez-Aguilar J. Rosales-García R. F. Escobar-Jiménez M. G. López-López V. M. Alvarado-Martínez V. H. Olivares-Peregrino |
| author_sort | J. F. Gómez-Aguilar |
| collection | DOAJ |
| description | 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)=ω0γγ1-γ, where ω0 is the fundamental frequency. For γ=3/2, the system is described by a third-order differential equation with frequency ω~ω03/2, and assuming γ=2 the dynamics are described by a fourth differential equation for jerk dynamics with frequency ω~ω02. |
| format | Article |
| id | doaj-art-0051c9490ef042979d379f8da8d05c15 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-0051c9490ef042979d379f8da8d05c152025-02-03T01:26:26ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/97404109740410On the Possibility of the Jerk Derivative in Electrical CircuitsJ. F. Gómez-Aguilar0J. Rosales-García1R. F. Escobar-Jiménez2M. G. López-López3V. M. Alvarado-Martínez4V. H. Olivares-Peregrino5CONACYT-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, 62490 Cuernavaca, MOR, MexicoDepartamento de Ingeniería Electrica, DICIS, Universidad de Guanajuato, Carretera Salamanca-Valle de Santiago, Km. 3.5 + 1.8 Km., Comunidad de Palo Blanco, Salamanca, GTO, MexicoCentro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, MOR, MexicoCentro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, MOR, MexicoCentro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, MOR, MexicoCentro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, MOR, MexicoA 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)=ω0γγ1-γ, where ω0 is the fundamental frequency. For γ=3/2, the system is described by a third-order differential equation with frequency ω~ω03/2, and assuming γ=2 the dynamics are described by a fourth differential equation for jerk dynamics with frequency ω~ω02.http://dx.doi.org/10.1155/2016/9740410 |
| spellingShingle | J. F. Gómez-Aguilar J. Rosales-García R. F. Escobar-Jiménez M. G. López-López V. M. Alvarado-Martínez V. H. Olivares-Peregrino On the Possibility of the Jerk Derivative in Electrical Circuits Advances in Mathematical Physics |
| title | On the Possibility of the Jerk Derivative in Electrical Circuits |
| title_full | On the Possibility of the Jerk Derivative in Electrical Circuits |
| title_fullStr | On the Possibility of the Jerk Derivative in Electrical Circuits |
| title_full_unstemmed | On the Possibility of the Jerk Derivative in Electrical Circuits |
| title_short | On the Possibility of the Jerk Derivative in Electrical Circuits |
| title_sort | on the possibility of the jerk derivative in electrical circuits |
| url | http://dx.doi.org/10.1155/2016/9740410 |
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