Geodesic
Integrable homogeneous dynamical systems with dissipation on the tangent bundles of four-dimensional manifolds. I. Equations of geodesic lines
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 77-95

Voir la notice de l'article provenant de la source Math-Net.Ru

In many problems of dynamics, systems arise whose position spaces are four-dimensional manifolds. Naturally, the phase spaces of such systems are the tangent bundles of the corresponding manifolds. Dynamical systems considered have variable dissipation, and the complete list of first integrals consists of transcendental functions expressed in terms of finite combinations of elementary functions. In this paper, we prove the integrability of more general classes of homogeneous dynamical systems with variable dissipation on tangent bundles of four-dimensional manifolds.
Keywords: dynamical system, nonconservative field, integrability, transcendental first integral. 
@article{INTO_2022_210_a8,
     author = {M. V. Shamolin},
     title = {Integrable homogeneous dynamical systems with dissipation on the tangent bundles of four-dimensional manifolds. {I.} {Equations} of geodesic lines},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {77--95},
     publisher = {mathdoc},
     volume = {210},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_210_a8/}
}
TY  - JOUR
AU  - M. V. Shamolin
TI  - Integrable homogeneous dynamical systems with dissipation on the tangent bundles of four-dimensional manifolds. I. Equations of geodesic lines
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 77
EP  - 95
VL  - 210
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_210_a8/
LA  - ru
ID  - INTO_2022_210_a8
ER  - 
%0 Journal Article
%A M. V. Shamolin
%T Integrable homogeneous dynamical systems with dissipation on the tangent bundles of four-dimensional manifolds. I. Equations of geodesic lines
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 77-95
%V 210
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_210_a8/
%G ru
%F INTO_2022_210_a8
M. V. Shamolin. Integrable homogeneous dynamical systems with dissipation on the tangent bundles of four-dimensional manifolds. I. Equations of geodesic lines. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 77-95. http://geodesic.mathdoc.fr/item/INTO_2022_210_a8/