Central Configurations Formed By Two Twisted Regular Polygons
Xiang Yu, Shiqing Zhang
TL;DR
This paper investigates the conditions under which two twisted regular polygons can form central configurations, extending previous symmetrical cases and proving limitations in more general settings.
Contribution
It provides necessary and sufficient conditions for central configurations of two twisted regular polygons and shows the non-existence of more configurations beyond specific cases.
Findings
Necessary and sufficient conditions established
No additional configurations in more general settings
Extension of previous symmetrical configuration results
Abstract
In this paper, we study the necessary conditions and sufficient conditions for the central configurations formed by two twisted regular polygons (one N-regular polygon and one L-regular polygon). We wish to extend the results of the symmetrical central configurations formed by two twisted N-regular polygons, however, it will be proved that there are not more central configurations in a more general setting than the central configurations considered for some more particular situations before.
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Taxonomy
TopicsMathematics and Applications · Advanced Differential Equations and Dynamical Systems · graph theory and CDMA systems