We will be concerned with the critical points of the oriented volume and Coulomb potential on configuration spaces of mechanical linkages. The case of a planar polygonal linkage will be considered in some detail. It will be shown that the critical points of the oriented area are given by the cyclic configurations and the critical values can be calculated using formulae of Heron-Brahmagupta type. Similar issues will be addressed in the case of Coulomb potential. Possible generalizations of these results for tensegrity linkages will be also outlined.
Extremal problems on configuration spaces of linkages
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