We begin by analyzing, using basic physics considerations, under what conditions it becomes energetically favorable to use aggressive regenerative braking to reach a lower speed over “coasting” where one relies solely on air drag to slow down. We then proceed to reformulate the question as an optimization problem to find the velocity profile that maximizes battery charge. Making a simplifying assumption on battery-charging efficiency, we express the recovered energy as an integral quantity, and we solve the associated Euler–Lagrange equation to find the optimal braking curves that maximize this quantity in the framework of variational calculus. Using Lagrange multipliers, we also explore the effect of adding a fixed-displacement constraint.

English, L.Q., A. Mareno, and Xuan-Lin Chen. Optimizing Regenerative Braking: A Variational Calculus Approach. Mathematical Problems in Engineering 2021 (2021): Article ID: 8002130, 8 pp. https://www.hindawi.com/journals/mpe/2021/8002130/

Copyright © 2021 L. Q. English et al.

This is an Open Access article distributed under the Creative Commons Attribution License, https://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Open access publication of this article was made possible with grant support from Waidner-Spahr Library distributed through the Dickinson College Research & Development Committee.

Lars English is a professor of Physics at Dickinson College.

This published version is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit Hindawi's Website. https://www.hindawi.com/journals/mpe/2021/8002130/