Abstract:
This paper is a survey of integrable cases in dynamics of two-, three-, and four-dimensional rigid bodies under the action of a nonconservative force field. We review both new results and results obtained earlier. Problems examined are described by dynamical systems with so-called variable dissipation with zero mean.
Citation:
M. V. Shamolin, “Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields”, Dynamical systems, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 125, VINITI, Moscow, 2013, 3–251; J. Math. Sci. (N. Y.), 204:4 (2015), 379–530
\Bibitem{Sha13}
\by M.~V.~Shamolin
\paper Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields
\inbook Dynamical systems
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2013
\vol 125
\pages 3--251
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into147}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 204
\issue 4
\pages 379--530
\crossref{https://doi.org/10.1007/s10958-014-2209-0}
Linking options:
https://www.mathnet.ru/eng/into147
https://www.mathnet.ru/eng/into/v125/p3
This publication is cited in the following 37 articles:
M. V. Shamolin, “Examples of Ninth-Order Integrable Dynamic Systems with Dissipation”, J Math Sci, 2025
M. V. Shamolin, “Examples of Integrable Equations of Motion of a Five-Dimensional Rigid Body in the Presence of Internal and External Force Fields”, J Math Sci, 2025
Maxim V. Shamolin, “On Integrability of Certain Classes of Variable Dissipation Systems”, PROOF, 4 (2024), 75
M. V. Shamolin, “Integriruemye dinamicheskie sistemy nechetnogo poryadka s dissipatsiei raznogo znaka”, Tr. sem. im. I. G. Petrovskogo, 33, Izdatelstvo Moskovskogo universiteta, M., 2023, 424–464
Maxim V. Shamolin, “Qualitative and Numerical Research of Body Motion in a Resisting Medium”, WSEAS TRANSACTIONS ON SYSTEMS, 20 (2021), 232
Maxim V. Shamolin, “Cases of Integrability Which Correspond to the Motion of a Pendulum in the Three-dimensional Space”, WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS, 16 (2021), 73
Maxim V. Shamolin, “Spatial motion of a pendulum in a jet flow: qualitative aspects and integrability”, Proc Appl Math and Mech, 20:1 (2021)
M. V. Shamolin, “Sistemy s dissipatsiei: otnositelnaya grubost, negrubost razlichnykh stepenei i integriruemost”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 70–82
M. V. Shamolin, “Sluchai integriruemykh dinamicheskikh sistem devyatogo poryadka s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 68–81
M. V. Shamolin, “Sluchai integriruemosti uravnenii dvizheniya pyatimernogo tverdogo tela pri nalichii vnutrennego i vneshnego silovykh polei”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 82–118
M. V. Shamolin, “Nekotorye integriruemye dinamicheskie sistemy nechetnogo poryadka s dissipatsiei”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 52–69
M. V. Shamolin, “Family of phase portraits in the spatial dynamics of a rigid body interacting with a resisting medium”, J. Appl. Industr. Math., 13:2 (2019), 327–339
M. V. Shamolin, “New Cases of Integrable Fifth-Order Systems with Dissipation”, Dokl. Phys., 64:4 (2019), 189
M. V. Shamolin, “Integrable Third and Fifth Order Dynamical Systems with Dissipation”, J Math Sci, 239:3 (2019), 412
M. V. Shamolin, “New Cases of Integrable Seventh-Order Systems with Dissipation”, Dokl. Phys., 64:8 (2019), 330
M. V. Shamolin, “Relative Structural Stability and Instability of Different Degrees in Systems with Dissipation”, J Math Sci, 239:3 (2019), 424
M. V. Shamolin, “A new case of an integrable system with dissipation on the tangent bundle of a multidimensional sphere”, Moscow University Mechanics Bulletin, 73:3 (2018), 51–59
M. V. Shamolin, “O dvizhenii mayatnika v mnogomernom prostranstve. Chast 3. Zavisimost polya sil ot tenzora uglovoi skorosti”, Vestn. SamU. Estestvennonauchn. ser., 24:2 (2018), 33–54
M. V. Shamolin, “Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres”, J. Math. Sci. (N. Y.), 250:6 (2020), 932–941
M. V. Shamolin, “Examples of Integrable Systems with Dissipation on the Tangent Bundles of Three-Dimensional Manifolds”, J. Math. Sci. (N. Y.), 250:6 (2020), 964–972
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