The slow-actuation limit for a rate-independent model of crawling locomotion
Venue: Paolo Gidoni - Aula Buzano (DISMA Politecnico di Torino)
The quasi-static limit is a convenient approximation in the modelling of several suitable mechanical systems, when the evolution occurs at a sufficiently slow time-scale. In this seminar, we discuss, by a mathematical perspective, the meaning of the quasi-static assumption in soft-bodied crawlers. First, we survey the relevance, or lack thereof, of inertia in some locomotion strategies. Then, we focus on a basic, but effective, family of models for soft crawlers and provide a mathematically rigorous derivation of the quasi-static regime. More precisely, we show the uniform convergence, for a slow-actuation limit, of solutions fo the dynamic model to those of a (quasi-static) rate-independent system. We conclude with a brief survey of related open problems.
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