Geodesic
Examples of integrable equations of motion of a five-dimensional rigid body in the presence of internal and external force fields
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 187 (2020), pp. 82-118

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In the study of integrable systems that describe multidimensional rigid bodies in nonconservative force fields, two approaches are used. The first approach is concerned with systems in which the nonconservativity of force fields is related to additional coefficients in the cinematical relations; note that $n=5$ and $n=6$ are special cases. The second approach is based on the simultaneous influence of two force fields: internal (conservative) and external (nonconservative). This paper is devoted to the special case where $n=5$.
Keywords: multidimensional rigid body, conservative force field, integrability, transcendental first integral.
Mots-clés : equations of motion 
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     author = {M. V. Shamolin},
     title = {Examples of integrable equations of motion of a five-dimensional rigid body in the presence of internal and external force fields},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {82--118},
     publisher = {mathdoc},
     volume = {187},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_187_a8/}
}
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M. V. Shamolin. Examples of integrable equations of motion of a five-dimensional rigid body in the presence of internal and external force fields. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 187 (2020), pp. 82-118. http://geodesic.mathdoc.fr/item/INTO_2020_187_a8/