  We introduce a method of exploring potential energy contours in complex
dynamical systems based on potentiostatic kinematics wherein the systems are
evolved with minimal changes to their potential energy. We construct a simple
iterative algorithm for performing potentiostatic kinematics, which uses an
estimate curvature to predict new configurations space coordinates on the
potential energy contour and a potentiostat term component to correct for
errors in prediction. Our methods are then applied to atomic structure models
using an interatomic potential for energy and force evaluations as would
commonly be invoked in a molecular dynamics simulation. Using several model
systems, we assess the stability and accuracy of the method on different
hyperparameters in the implementation of the potentiostatic kinematics. Our
implementation is open source and available within the Atomic Simulation
Environment (ASE) package for atomic simulation.
