Year: 2026
Type: preprint
Abstract: We use tools from nonlinear algebra to study the equilibria of small linear translational spring networks. Specifically we use the techniques of homotopy continuation, monodromy, and parameter homotopy (a.k.a. cheater homotopy) to solve all rigid linear translational spring networks up to $5$ nodes in both $2$ and $3$ dimensions. We describe a method of implementing parameter homotopy that arises naturally from the physical structure of the system. We give precise total degree bounds on the maximum number of solutions for general planar spring networks. We discuss further efficiency gains obtained from polyhedral homotopy methods. We compare the computation efficiency of these techniques against a baseline of Newton's method.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Air Force Research Laboratory
Award: G3580923641
OpenAlex ID: W7208709180