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Found 62 Documents (Results 1–62)

Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications. (English. Russian original) Zbl 1416.70009

J. Math. Sci., New York 230, No. 2, 185-353 (2018); translation from Fundam. Prikl. Mat. 20, No. 4, 3-231 (2015).
MSC:  70E45 70E40 37J05
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The case of integrable systems with dissipation on the tangent bundle of a multidimensional sphere. (English. Russian original) Zbl 1404.37071

J. Math. Sci., New York 228, No. 6, 723-730 (2018); translation from Probl. Mat. Anal. 90, 107-113 (2018).
MSC:  37J35 70E40 70E45
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On the completeness of the Manakov integrals. (English. Russian original) Zbl 1404.37068

J. Math. Sci., New York 223, No. 6, 675-685 (2017); translation from Fundam. Prikl. Mat. 20, No. 2, 35-49 (2015).
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Classification of integrable cases in the dynamics of a four-dimensional rigid body in a nonconservative field in the presence of a tracking force. (English. Russian original) Zbl 1346.70007

J. Math. Sci., New York 204, No. 6, 808-870 (2015); translation from Sovrem. Mat. Prilozh. 88 (2013).
MSC:  70E45 70E40
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Some classes of integrable problems in spatial dynamics of a rigid body in a nonconservative force field. (English. Russian original) Zbl 1353.70020

J. Math. Sci., New York 210, No. 3, 292-330 (2015); translation from Tr. Semin. Im. I. G. Petrovskogo 30, No. 2, 287-350 (2014).
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Variety of integrable cases in dynamics of low- and multi-dimensional rigid bodies in nonconservative force fields. (English. Russian original) Zbl 1353.70019

J. Math. Sci., New York 204, No. 4, 379-530 (2015); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 125, 5-254 (2013).
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Levi-Civita symbols, generalized vector products, and new integrable cases in mechanics of multidimensional bodies. (English. Russian original) Zbl 1278.70007

J. Math. Sci., New York 187, No. 3, 280-299 (2012); translation from Sovrem. Mat. Prilozh. 76 (2012).
MSC:  70E40 70E45 37J35
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WITHDRAWN: On the stability problem and a bifurcation phenomenon for a special class of equilibria of the free rigid body on \(\mathfrak{so}(5)\). arXiv:1103.5583

Preprint, arXiv:1103.5583 [math.DS] (2011); retraction notice ibid.
MSC:  34D20 70E17 70E45
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Classification of complete integrability cases in four-dimensional symmetric rigid-body dynamics in a nonconservative field. (English. Russian original) Zbl 1288.70001

J. Math. Sci., New York 165, No. 6, 743-754 (2010); translation from Sovrem. Mat. Prilozh. 65, 1311-141 (2009).
MSC:  70E45 70E15 70H06
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The case of complete integrability in the dynamics of a four-dimensional rigid body in a nonconservative field. (English. Russian original) Zbl 1356.70010

Russ. Math. Surv. 65, No. 1, 183-185 (2010); translation from Usp. Mat. Nauk. 65, No. 1, 189-190 (2010).
MSC:  70E40 70E45
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On integrability and rigid-body systems. (English) Zbl 1289.37033

Dragovich, B.(ed.) et al., Proceedings of the 2nd summer school in modern mathematical physics, Kopaonik, Yugoslavia, September 1–12, 2002. Belgrade: Institute of Physics (ISBN 86-82441-13-6). Sveske Fizičkikh Nauka. Series A: Conferences 16, 1, 533-548 (2003).
MSC:  37J35 14H70 70E45
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Modern methods in the theory of integrable systems. Bi-Hamiltonian description, Lax representation, and separation of variables. (Современные методы теории интегрируемых систем. Бигамильтоново описание, представление Лакса, разделение переменных.) (Russian) Zbl 1101.37041

Sovremennaya Matematika. Izhevsk: Institut Komp’yuternykh Issledovaniĭ (ISBN 5-93972-219-9/hbk). 295 p. (2003).
MSC:  37-02 70-02 37J35 37K05 37K10 70H06 70E45
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Special shaky and overclosed mechanisms. (Spezielle wackelige and übergeschlossene Mechanismen.) (German) Zbl 0963.70518

Röschel, O. (ed.) et al., Geometrie-Tagung “107 Jahre Drehfluchtprinzip”, Vorau, Österreich, 1. Juni-6. Juni 1997. Tagungsband. Vorau: TU Graz, 94 (1999).
MSC:  70B15 70E45 52C25
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A generalized Poinsot interpretation of the motion of a multidimensional rigid body. (English. Russian original) Zbl 0963.70525

Proc. Steklov Inst. Math. 205, 181-186 (1995); translation from Tr. Mat. Inst. Steklova 205, 200-206 (1994).
MSC:  70E45 70E05
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