Geodesic
Integrable systems in planar robotics
Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 320-340

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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. 
@article{CHEB_2020_21_2_a22,
     author = {T. S. Ratiu and Nguyen Tien Zung},
     title = {Integrable systems in planar robotics},
     journal = {\v{C}eby\v{s}evskij sbornik},
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     publisher = {mathdoc},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a22/}
}
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T. S. Ratiu; Nguyen Tien Zung. Integrable systems in planar robotics. Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 320-340. http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a22/