Geodesic
On a pendulum motion in multi-dimensional space. Part 2. Independence of force fields on the tensor of angular velocity
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2017), pp. 40-67 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the proposed cycle of work, we study the equations of the motion of dynamically symmetric fixed $n$-dimensional rigid bodies-pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of the motion of a free $n$-dimensional rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint. In this work, we study the case of independence of force fields on the tensor of angular velocity.
Keywords: multi-dimensional rigid body, non-conservative force field, dynamical system, case of integrability. 
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     title = {On a pendulum motion in multi-dimensional space. {Part} 2. {Independence} of force fields on the tensor of angular velocity},
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M. V. Shamolin. On a pendulum motion in multi-dimensional space. Part 2. Independence of force fields on the tensor of angular velocity. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2017), pp. 40-67. http://geodesic.mathdoc.fr/item/VSGU_2017_4_a4/

[1] Shamolin M. V., “Cases of integrability corresponding to the pendulum motion on the plane”, Vestnik of Samara State University. Natural Science Series, 2015, no. 10(132), 91–113 (in Russian)

[2] Shamolin M. V., “Cases of integrability corresponding to the pendulum motion on the three-dimensional space”, Vestnik of Samara State University. Natural Science Series, 2016, no. 3–4, 75–97 (in Russian)

[3] Shamolin M. V., “Variety of cases of integrability in dynamics of lower-, and multi-dimensional body in nonconservative field”, Dinamicheskie sistemy, Itogi nauki i tekhniki. Ser.: “Sovremennaia matematika i ee prilozheniia. Tematicheskie obzory”, 125, 2013, 5–254 (in Russina)

[4] Pokhodnya N. V., Shamolin M. V., “Some cases of integrability of dynamic systems in transcedent functions”, Vestnik of Samara State University. Natural Science Series, 2013, no. 9/1(110), 35–41 (in Russian)

[5] Shamolin M. V., “New Cases of Integrable Systems with Dissipation on the Tangent Bundle of a Three-Dimensional Manifold”, Physics Doklady, 477:2 (2017), 168–172 (in Russian)

[6] Shamolin M. V., “Complete List of First Integrals of Dynamic Equations for a Multidimensional Solid in a Nonconservative Field”, Physics Doklady, 461:5 (2015), 533–536 (in Russian) | DOI

[7] Arnold V. I., Kozlov V. V., Neyshtadt A. I., Mathematical aspects in classical and celestial mechanics, VINITI, M., 1985, 304 p pp. (in Russian) | MR

[8] Trofimov V. V., “Symplectic structures on symmetruc spaces automorphysm groups”, Moscow University Mathematics Bulletin, 1984, no. 6, 31–33 (in Russian)

[9] Trofimov V. V., Shamolin M. V., “Geometrical and dynamical invariants of integrable Hamiltonian and dissipative systems”, Journal of Mathematical Sciences, 16:4 (2010), 3–229 (in Russian)

[10] Shamolin M.V., “Mnogomernyi mayatnik v nekonservativnom silovom pole”, Doklady RAN, 460:2 (2015), 165–169 ; Shamolin M. V., Methods of analysis of various dissipation dynamical systems in dynamics of a rigid body, Izd-vo ”Ekzamen”, M., 2007, 352 pp. (in Russian) | DOI | MR

[11] Shamolin M.V., “Novyi sluchai integriruemosti v dinamike mnogomernogo tverdogo tela v nekonservativnom pole”, Doklady RAN, 453:1 (2013), 46–49 ; Shamolin M. V., “Some model problems of dynamics for a rigid body interacting with a medium”, International Applied Mechanics, 43:10 (2007), 49–67 (in Russian) | DOI | DOI | MR

[12] Shamolin M. V., “New Cases of Integrable Systems with Dissipation on Tangent Bundles of Two- and ThreeDimensional Spheres”, Physics Doklady, 471:5 (2016), 547–551 (in Russian) | DOI | MR

[13] Shamolin M. V., “New Cases of Integrable Systems with Dissipation on a Tangent Bundle of a Multidimensional Sphere”, Physics Doklady, 474:2 (2017), 177–181 (in Russian) | DOI | MR

[14] Shamolin M. V., “New Cases of Integrable Systems with Dissipation on a Tangent Bundle of a Two-Dimensional Manifold”, Physics Doklady, 475:5 (2017), 519–523 (in Russian)