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Chebyshevskii Sbornik, 2020, Volume 21, Issue 2, Pages 320–340
DOI: https://doi.org/10.22405/2226-8383-2018-21-2-320-340 (Mi cheb912) 		 
Integrable systems in planar robotics

T. S. Ratiuabc, Nguyen Tien Zungd

a 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)
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DOI: https://doi.org/10.22405/2226-8383-2018-21-2-320-340
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.
Funding agency Grant number
National Natural Science Foundation of China 11871334
Swiss National Science Foundation NCCR SwissMAP
Received: 09.01.2019
Accepted: 11.03.2020
Document Type: Article
UDC: 514.85+531.2+531.012
Language: English
Citation: T. S. Ratiu, Nguyen Tien Zung, “Integrable systems in planar robotics”, Chebyshevskii Sb., 21:2 (2020), 320–340
Citation in format AMSBIB
\Bibitem{RatZun20}
\by T.~S.~Ratiu, Nguyen~Tien~Zung
\paper Integrable systems in planar robotics
\jour Chebyshevskii Sb.
\yr 2020
\vol 21
\issue 2
\pages 320--340
\mathnet{http://mi.mathnet.ru/cheb912}
\crossref{https://doi.org/10.22405/2226-8383-2018-21-2-320-340}
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