Integrable systems in planar robotics

T. S. Ratiu^abc, Nguyen Tien Zung<sup>d

a</sup> School of Mathematical Sciences, Shanghai Jiao Tong University (Shanghai, China)
^b Section de mathématiques, Université de Genéve (Genéve, Switzerland)
^c École Polytechnique Fédérale de Lausanne (Lausanne, Switzerland)
^d Institut de Mathématiques de Toulouse (Toulouse, France)

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.

Keywords: planar linkage, commuting flows, non-Hamiltonian integrability, volume form, Nambu structure, cross-product of integrable systems.

UDC: 514.85+531.2+531.012

Received: 09.01.2019
Accepted: 11.03.2020

Language: English

DOI: 10.22405/2226-8383-2018-21-2-320-340