English

Integrable systems in planar robotics

Dynamical Systems 2019-09-24 v1

Abstract

The main purpose of this paper is to investigate commuting flows and integrable systems on the configuration spaces of planar linkages. Our study leads to the definition of a natural volume form on each configuration space of planar linkages, the notion of cross products of integrable systems, and also the notion of multi-Nambu integrable systems. The first integrals of our systems are functions of Bott-Morse type, which may be used to study the topology of configuration spaces. Dedicated to Anatoly T. Fomenko on the occasion of his 75th birthday

Cite

@article{arxiv.1909.09707,
  title  = {Integrable systems in planar robotics},
  author = {Tudor S. Ratiu and Nguyen Tien Zung},
  journal= {arXiv preprint arXiv:1909.09707},
  year   = {2019}
}

Comments

20 pages, 10 figures

R2 v1 2026-06-23T11:21:53.405Z