On experimentally locating saddle-points on a potential energy surface from observed dynamics

TitleOn experimentally locating saddle-points on a potential energy surface from observed dynamics
Publication TypeJournal Article
Year of Publication2019
AuthorsY Xu, LN Virgin, and SD Ross
JournalMechanical Systems and Signal Processing
Volume130
Start Page152
Pagination152 - 163
Date Published09/2019
Abstract

This paper details a new method to estimate the location of unstable equilibria, specifically saddle-points, based on transient trajectories from experiments. We describe a system in which saddle-points (not easily observed in a direct sense)influence the behavior of trajectories that pass ’close-by’ them. This influence is used to construct a model and thus identify a more accurate estimate of the location using a number of refinements associated with linearization and regression. Both simulations and experiments were conducted to verify the method. The experiment consists of a small ball rolling on a relatively shallow curved surface under the influence of gravity: a potential energy surface in two dimensions. Tracking the motion of the ball with a digital camera provides data that compares closely with the output of numerical simulation. The experimental results suggest that this method can effectively locate the saddle equilibria in a system, and the robustness of the approach is assessed relative to the effect of noise, size of the local neighborhood, etc., in addition to providing information on the local dynamics. Given the relative simplicity of the experiment system used and a priori knowledge of the saddle-points, it is a useful testing environment for system identification in a nonlinear context.

DOI10.1016/j.ymssp.2019.05.002
Short TitleMechanical Systems and Signal Processing