Integrable Systems with Dissipation on the Tangent Bundles of 2- and 3-Dimensional Spheres

被引：0

作者：

Shamolin M.V. ^{[1
]}

机构：

[1] M. V. Lomonosov Moscow State University, Moscow

来源：

Journal of Mathematical Sciences | 2020年 / 245卷 / 4期

基金：

俄罗斯基础研究基金会;

关键词：

70E18; dissipation; dynamical system; integrability; transcendental first integral;

D O I：

10.1007/s10958-020-04706-3

中图分类号：

学科分类号：

摘要：

In this paper, we prove the explicit integrability of certain classes of dynamical systems on the tangent bundles of 2- and 3-dimensional spheres in the case where the forces are fields with so-called variable dissipation. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：498 / 507

页数：9

共 30 条

[21]

Shamolin M.V., A new case of integrability in the dynamics of a four-dimensional rigid body in a nonconservative field, Dokl. Ross. Akad. Nauk, 437, 2, pp. 190-193, (2011)

[22]

Shamolin M.V., A complete list of first integrals in the problem of the motion of a fourdimensional rigid body in a nonconservative field in the presence of linear damping, Dokl. Ross. Akad. Nauk, 440, 2, pp. 187-190, (2011)

[23]

Shamolin M.V., A new case of integrability in the dynamics of a four-dimensional rigid body in a nonconservative field in the presence of linear damping, Dokl. Ross. Akad. Nauk, 444, 5, pp. 506-509, (2012)

[24]

Shamolin M.V., A new case of integrability in the spatial dynamics of a rigid body interacting with a medium, taking into account linear damping, Dokl. Ross. Akad. Nauk, 442, 4, pp. 479-481, (2012)

[25]

Shamolin M.V., Comparison of complete integrability cases in dynamics of a two-, three-, and four-dimensional rigid body in a nonconservative field, J. Math. Sci., 187, 3, pp. 346-359, (2012)

[26]

Shamolin M.V., Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields, J. Math. Sci., 204, 4, pp. 379-530, (2015)

[27]

Shamolin M.V., Integrable systems with variable dissipation on the tangent bundle to a multidimensional sphere and applications, Fundam. Prikl. Mat., 20, 4, pp. 3-231, (2015)

[28]

Shamolin M.V., Low- and multidimensional pendulums in nonconservative field. Part 1, J. Math. Sci., 233, 2, pp. 173-299, (2018)

[29]

Shamolin M.V., Low- and multidimensional pendulums in nonconservative field. Part 1, J. Math. Sci., 233, 3, pp. 301-397, (2018)

[30]

Trofimov V.V., Shamolin M.V., Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems, Fundam. Prikl. Mat., 16, 4, pp. 3-229, (2010)

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