Point Charges and Polygonal Linkages

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• 作者：Giorgi Khimshiashvili ; Gaiane Panina…
• 关键词：Mechanical linkage ; Configuration space ; Moduli space ; Coulomb potential ; Cayley ; Menger determinant ; Coulomb control
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：23
• 期：1
• 页码：1-17
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Vibration, Dynamical Systems, Control; Calculus of Variations and Optimal Control; Optimization; Analysis; Applications of Mathematics; Systems Theory, Control;
• 出版者：Springer US
• ISSN：1573-8698
• 卷排序：23

文摘

We investigate the critical points of Coulomb potential of point charges placed at the vertices of a planar polygonal linkage. It is shown that, for a collection of positive charges on a pentagonal linkage, there is a unique critical point in the set of convex configurations which is the point of absolute minimum. This enables us to prove that two controlling charges are sufficient to navigate between any two convex configurations of a pentagonal linkage.