Invariant Volume Forms of Variable Dissipation Systems with Three Degrees of Freedom

被引：3

作者：

Shamolin, M. V. ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow, Russia

来源：

DOKLADY MATHEMATICS | 2022年 / 106卷 / 03期

关键词：

dynamical system; integrability; dissipation; transcendental first integral; invariant differential form; INTEGRABILITY;

D O I：

10.1134/S1064562422700168

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Tensor invariants (differential forms) for homogeneous dynamical systems on tangent bundles of smooth three-dimensional manifolds are presented. The connection between the presence of these invariants and the full set of first integrals necessary for the integration of geodesic, potential, and dissipative systems is shown. The introduced force fields make the considered systems dissipative with dissipation of different signs and generalize previously considered fields.

引用

页码：479 / 484

页数：6

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