We consider differential systems obtained by coupling two Euler–Poinsot systems. The motivation to consider such systems can be traced back to the Riemann ellipsoid problem. We provide new cases for which these systems are completely integrable. We also prove that these systems either are completely integrable or have at most four functionally independent analytic first integrals.
DOI : 10.1051/cocv/2015035
Mots clés : Polynomial first integrals, homogeneous differential systems, Riemann ellipsoid problem, Euler–Poinsot systems, complete integrability
@article{COCV_2016__22_3_872_0,
author = {Llibre, Jaume and Valls, Cl\`audia},
title = {On the polynomial integrability of a system motivated by the {Riemann} ellipsoid problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {872--882},
publisher = {EDP-Sciences},
volume = {22},
number = {3},
year = {2016},
doi = {10.1051/cocv/2015035},
zbl = {1346.34002},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2015035/}
}
TY - JOUR AU - Llibre, Jaume AU - Valls, Clàudia TI - On the polynomial integrability of a system motivated by the Riemann ellipsoid problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 872 EP - 882 VL - 22 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2015035/ DO - 10.1051/cocv/2015035 LA - en ID - COCV_2016__22_3_872_0 ER -
%0 Journal Article %A Llibre, Jaume %A Valls, Clàudia %T On the polynomial integrability of a system motivated by the Riemann ellipsoid problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 872-882 %V 22 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2015035/ %R 10.1051/cocv/2015035 %G en %F COCV_2016__22_3_872_0
Llibre, Jaume; Valls, Clàudia. On the polynomial integrability of a system motivated by the Riemann ellipsoid problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 872-882. doi : 10.1051/cocv/2015035. http://www.numdam.org/articles/10.1051/cocv/2015035/
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