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Second-order prestress stability and third-order rigidity of polyhedral surfaces
Zeyuan He
https://arxiv.org/abs/2506.22019 https://a…

Second-order prestress stability and third-order rigidity of polyhedral surfaces
The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to polyhedral surfaces, we derive new criterion for testing second-order prestress stability. Additionally, we discuss the limitations of testing third-order rigidity, except in the special case where the null space of the rigidity matrix is one-dimensional. Altho…