TY - GEN
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 -