Catastrophe discriminants of tensegrity frameworks
Alex Heaton (The Fields Institute)
Abstract: We discuss elastic tensegrity frameworks made from rigid bars and elastic cables, depending on many parameters. For any fixed parameter values, the stable equilibrium position of the framework is determined by minimizing an energy function subject to algebraic constraints. As parameters smoothly change, it can happen that a stable equilibrium disappears. This loss of equilibrium is called `catastrophe' since the framework will experience large-scale shape changes despite small changes of parameters. Using nonlinear algebra we characterize a semialgebraic subset of the parameter space, the catastrophe set, which detects the merging of local extrema from this parametrized family of constrained optimization problems, and hence detects possible catastrophe. Tools from numerical nonlinear algebra allow reliable and efficient computation of all stable equilibrium positions as well as the catastrophe set itself.
algebraic geometrynumber theory
Audience: researchers in the topic
Series comments: Description: Research/departmental seminar
Seminar usually meets in-person. For online editions, the Zoom link is shared via mailing list.
Organizers: | Katrina Honigs*, Nils Bruin* |
*contact for this listing |