Integrable systems in planar robotics

Friday, 20 September, 2019

Published in: 

arXiv:1909.09707

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

Author(s): 

Tudor S. Ratiu
Nguyen Tien Zung