Geodesic
Systems with four degrees of freedom with dissipation: analysis and integrability
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 205 (2022), pp. 55-94

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This paper is a survey on integrable systems with four degrees of freedom whose phase spaces are tangent bundles of four-dimensional smooth manifolds. First, we discuss in detail the original problem from the dynamics of a multidimensional rigid body in a nonconservative force field; then we consider general dynamical systems on the tangent bundles of a sufficiently large class of smooth manifolds and prove sufficient conditions for the integrability of the dynamical systems considered in the class of transcendental.
Keywords: dynamical system, integrability, transcendental first integral. 
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     author = {M. V. Shamolin},
     title = {Systems with four degrees of freedom with dissipation: analysis and integrability},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {55--94},
     publisher = {mathdoc},
     volume = {205},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_205_a4/}
}
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M. V. Shamolin. Systems with four degrees of freedom with dissipation: analysis and integrability. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 205 (2022), pp. 55-94. http://geodesic.mathdoc.fr/item/INTO_2022_205_a4/