3 papers
math.OC2022
Singularly Perturbed Averaging with Application to Bio-Inspired 3D Source Seeking
Mahmoud Abdelgalil, Asmaa Eldesoukey, Haithem Taha
We analyze a class of singularly perturbed high-amplitude, high-frequency oscillatory systems that arises in extremum seeking applications. We provide explicit formulas for averagi…
math.OC2022
Recursive Averaging with Application to Bio-Inspired 3D Source Seeking
Mahmoud Abdelgalil, Haithem Taha
We analyze a class of high-amplitude, high-frequency oscillatory systems in which periodicity occurs on two distinct time scales and establish the convergence of its trajectories t…
physics.flu-dyn2021
A Variational Theory of Lift
Cody Gonzalez, Haithem E. Taha
In this paper, we revive a special, less-common, variational principle in analytical mechanics (Hertz' principle of least curvature) to develop a novel variational analogue of Eule…