Stability and Trajectories Analysis of a Fractional Generalization of Simple Pendulum Dynamic Equation

Ibrahima Ndoye; Taous-Meriem Laleg Kirati

doi:10.23919/ecc.2019.8795821

Stability and Trajectories Analysis of a Fractional Generalization of Simple Pendulum Dynamic Equation

Ibrahima Ndoye, Taous-Meriem Laleg Kirati

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

Abstract

In this paper, we present the dynamics of the simple pendulum by using the fractional-order derivatives. Equations of motion are proposed for cases without input and external forcing. We use the fractional-order Euler-Lagrange equations to obtain the fractional-order dynamic equation of the simple pendulum. We perform equilibria analysis, indicate the conditions where stability dynamics can be observed for both integer and fractional-order models. Finally, phase diagrams have been plotted to visualize the effect of the fractional-order derivatives.

Original language	English (US)
Title of host publication	2019 18th European Control Conference (ECC)
Publisher	IEEE
Pages	3854-3860
Number of pages	7
ISBN (Print)	9783907144008
DOIs	https://doi.org/10.23919/ecc.2019.8795821
State	Published - Aug 15 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research reported herein is supported by the King Abdullah University of Science and Technology (KAUST).

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10.23919/ecc.2019.8795821

https://repository.kaust.edu.sa/bitstream/10754/656576/1/IEEE_ECC_2019.pdf

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@inproceedings{377653b9eecc4a0fac6b359b01885ef0,

title = "Stability and Trajectories Analysis of a Fractional Generalization of Simple Pendulum Dynamic Equation",

abstract = "In this paper, we present the dynamics of the simple pendulum by using the fractional-order derivatives. Equations of motion are proposed for cases without input and external forcing. We use the fractional-order Euler-Lagrange equations to obtain the fractional-order dynamic equation of the simple pendulum. We perform equilibria analysis, indicate the conditions where stability dynamics can be observed for both integer and fractional-order models. Finally, phase diagrams have been plotted to visualize the effect of the fractional-order derivatives.",

author = "Ibrahima Ndoye and Kirati, {Taous-Meriem Laleg}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The research reported herein is supported by the King Abdullah University of Science and Technology (KAUST).",

year = "2019",

month = aug,

day = "15",

doi = "10.23919/ecc.2019.8795821",

language = "English (US)",

isbn = "9783907144008",

pages = "3854--3860",

booktitle = "2019 18th European Control Conference (ECC)",

publisher = "IEEE",

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T1 - Stability and Trajectories Analysis of a Fractional Generalization of Simple Pendulum Dynamic Equation

AU - Ndoye, Ibrahima

AU - Kirati, Taous-Meriem Laleg

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The research reported herein is supported by the King Abdullah University of Science and Technology (KAUST).

PY - 2019/8/15

Y1 - 2019/8/15

N2 - In this paper, we present the dynamics of the simple pendulum by using the fractional-order derivatives. Equations of motion are proposed for cases without input and external forcing. We use the fractional-order Euler-Lagrange equations to obtain the fractional-order dynamic equation of the simple pendulum. We perform equilibria analysis, indicate the conditions where stability dynamics can be observed for both integer and fractional-order models. Finally, phase diagrams have been plotted to visualize the effect of the fractional-order derivatives.

AB - In this paper, we present the dynamics of the simple pendulum by using the fractional-order derivatives. Equations of motion are proposed for cases without input and external forcing. We use the fractional-order Euler-Lagrange equations to obtain the fractional-order dynamic equation of the simple pendulum. We perform equilibria analysis, indicate the conditions where stability dynamics can be observed for both integer and fractional-order models. Finally, phase diagrams have been plotted to visualize the effect of the fractional-order derivatives.

UR - http://hdl.handle.net/10754/656576

UR - https://ieeexplore.ieee.org/document/8795821/

UR - http://www.scopus.com/inward/record.url?scp=85071581786&partnerID=8YFLogxK

U2 - 10.23919/ecc.2019.8795821

DO - 10.23919/ecc.2019.8795821

M3 - Conference contribution

SN - 9783907144008

SP - 3854

EP - 3860

BT - 2019 18th European Control Conference (ECC)

PB - IEEE

ER -

Stability and Trajectories Analysis of a Fractional Generalization of Simple Pendulum Dynamic Equation

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