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math.MG2025
A Constrained Optimization Approach for Constructing Rigid Bar Frameworks with Higher-order Rigidity
Xuenan Li, Christian D. Santangelo, Miranda Holmes-Cerfon
We present a systematic approach for constructing bar frameworks that are rigid but not first-order rigid, using constrained optimization. We show that prestress stable (but not fi…
math.MG2025
Higher Order Rigidity and Energy
Steven J. Gortler, Miranda Holmes-Cerfon, Louis Theran
In this paper, we revisit the notion of higher-order rigidity of a bar-and-joint framework. In particular, we provide a link between the rigidity properties of a framework, and the…