On experimentally locating saddle-points on a potential energy surface from observed dynamics
On experimentally locating saddle-points on a potential energy surface from observed dynamics
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DOI：
10.1016/j.ymssp.2019.05.002
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发表时间：
2019-09
影响因子：
8.4
通讯作者：
Yawen Xu;L. Virgin;S. Ross
中科院分区：
文献类型：
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作者：
Yawen Xu;L. Virgin;S. Ross
本文详细介绍了一种新的方法来估计不稳定平衡点的位置，特别是鞍点，基于瞬态轨迹的实验。我们描述了一个系统，其中鞍点（不容易在直接意义上观察到）影响通过“靠近”它们的轨迹的行为。利用这种影响来构建模型，从而利用与线性化和回归相关的一些改进来确定更准确的位置估计。通过仿真和实验验证了该方法的有效性。实验包括一个小球在重力作用下在一个相对较浅的曲面上滚动：一个二维的势能面。用数码相机跟踪球的运动提供的数据与数值模拟的输出结果非常接近。实验结果表明，该方法可以有效地定位系统中的鞍态平衡点，并且除了提供局部动态信息外，还可以相对于噪声、局部邻域大小等影响评估该方法的鲁棒性。考虑到实验系统的相对简单性和鞍点的先验知识，它是非线性环境下系统识别的有用测试环境。
This paper details a new method to estimate the location ofunstableequilibria, 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.