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Low-Dimensional and Multi-Dimensional Pendulums in Nonconservative Fields. Part 2

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Abstract

In this review, we discuss new cases of integrable systems on the tangent bundles of finite-dimensional spheres. Such systems appear in the dynamics of multidimensional rigid bodies in non-conservative fields. These problems are described by systems with variable dissipation with zero mean. We found several new cases of integrability of equations of motion in terms of transcendental functions (in the sense of the classification of singularities) that can be expressed as finite combinations of elementary functions.

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  228. M. V. Shamolin, “The cases of integrability in terms of transcendental functions in dynamics of a rigid body interacting with a medium,” in: Proc. 9th Conf. Dynamical Systems: Theory and Applications (DSTA 2007), Lodz, Poland, December 17–20, 2007, 1, Technical Univ. Lodz (2007), pp. 415–422.

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  231. M. V. Shamolin, “The various cases of complete integrability in dynamics of a rigid body interacting with a medium,” in: CD Proc. Conf. Multibody Dynamics, ECCOMAS Thematic Conf. Warsaw, Poland, June 29–July 2, 2009, Polish Acad. Sci., Warsaw (2009), pp. 1–20.

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  236. M. V. Shamolin, “Variety of the cases of integrability in dynamics of a 2D-, 3D-, and 4Drigid body interacting with a medium,” in: Proc. 11th Conf. Dynamical Systems: Theory and Applications (DSTA 2011), Lodz, Poland, December 5–8, 2011, Technical Univ. Lodz (2011), pp. 11–24.

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  239. M. V. Shamolin, “Variety of the cases of integrability in Dynamics of a symmetric 2D-, 3D- and 4D-rigid body in a nonconservative field,” Int. J. Struct. Stabil. Dynam., 13, No. 7, 1340011–1340024 (2013).

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  241. M. V. Shamolin, “New cases of integrability in multidimensional dynamics in a nonconservative field,” in: CD Proc. XLII Summer School-Conf. “Advanced Problems in Mechanics” (APM 2014), June 30–July 5, 2014, St. Petersburg (Repino), Russia [in Russian], St. Petersburg (2014), pp. 435–446.

  242. M. V. Shamolin, “Dynamical pendulum-like nonconservative systems,” in: Applied Non-Linear Dynamical Systems, Springer Proc. Math. Stat., 93, 503–525 (2014).

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  246. M. V. Shamolin, “Multidimensional pendulum in a nonconservative force field,” in: CD Proc. XLIII Summer School-Conf. “Advances Problems in Mechanics” (APM 2015), June 22–27, 2015, St. Petersburg, Russia [in Russian], St. Petersburg (2015), pp. 322–332.

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Shamolin, M.V. Low-Dimensional and Multi-Dimensional Pendulums in Nonconservative Fields. Part 2. J Math Sci 233, 301–397 (2018). https://doi.org/10.1007/s10958-018-3934-6

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