Optimizing Regenerative Braking: A Variational Calculus Approach

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