Geodesic
Low-dimensional and multi-dimensional pendulums in nonconservative fields. Part~1
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Dynamical systems, Tome 134 (2017), pp. 6-128

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In this review, we discuss new cases of integrable systems on the tangent bundles of finite-dimensional spheres. Such systems appear in the dynamics of multidimensional rigid bodies in nonconservative fields. These problems are described by systems with variable dissipation with zero mean. We found several new cases of integrability of equations of motion in terms of transcendental functions (in the sense of the classification of singularities) that can be expressed as finite combinations of elementary functions.
Keywords: fixed rigid body, pendulum, multi-dimensional body, integrable system, variable dissipation system, transcendental first integral. 
@article{INTO_2017_134_a1,
     author = {M. V. Shamolin},
     title = {Low-dimensional and multi-dimensional pendulums in nonconservative fields. {Part~1}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {6--128},
     publisher = {mathdoc},
     volume = {134},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_134_a1/}
}
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M. V. Shamolin. Low-dimensional and multi-dimensional pendulums in nonconservative fields. Part~1. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Dynamical systems, Tome 134 (2017), pp. 6-128. http://geodesic.mathdoc.fr/item/INTO_2017_134_a1/