A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers

2020/07/17 by Paolo Gidoni, Filippo Riva
Engineering · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Applied mathematics #Classical mechanics #Computer science #Convergence (economics) #Dissipation #Inertia #Mathematical analysis #Mathematics #Micro and Nano Robotics #Modular Robots and Swarm Intelligence #Physics #Quasistatic process #Rate of convergence #Statistical physics #Translation (biology) #math-ph #math.MP #msc:49J40 #msc:49S05 #msc:70F40 #msc:70G75 #msc:74C05

paper · pdf · doi:10.1007/s00526-021-02067-6

published as Calculus of Variations and Partial Differential Equations 60 (2021), art. 191

arxiv created 2020/07/17 · openalex publication_date 2021/08/03 · arxiv updated 2021/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the approximation of quasistatic evolutions, formulated as abstract finite-dimensional rate-independent systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamical solutions to the quasistatic one, employing the concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy.

Citations

• Estimating dinosaur maximum running speeds using evolutionary robotics
• Soft robotics: a bioinspired evolution in robotics
• Crawling scallop: Friction-based locomotion with one degree of freedom
• Froude and the contribution of naval architecture to our understanding of bipedal locomotion
• Kinematic scaling of locomotion by hydrostatic animals: ontogeny of peristaltic crawling by the earthworm Lumbricus terrestris
• On the genesis of directional friction through bristle-like mediating elements