Abstract:
The author returns to construction of nonlinear mathematical model of the planar interaction of a medium to the rigid body was constructed. That model takes into account the dependency of shoulder of force from effective angular velocity of the body (the type of Strouhal number). In this case the moment of force of the interaction itself is also function of the angle of attack. As it has shown for processing the experiment on the motion of the uniform circular cylinders in water, these facts necessary to take into account at modeling. At study of flat model of the interaction of the rigid body with a medium the new cases of full integrability in elementary functions are found that has allowed to find the qualitative analogies between the free moving bodies in a resisting medium and the oscillations of bolted bodies in a jet flow. The comparison of phase patterns obtained under studying of nonlinear model of medium interaction, and the real vortex streets obtained by Karman, is occurred.
Keywords:
rigid body, resisting medium, jet flow, full integrability.
Citation:
M. V. Shamolin, “Rigid body motion in a resisting medium modelling and analogues with vortex streets”, Mat. Model., 27:1 (2015), 33–53; Math. Models Comput. Simul., 7:4 (2015), 389–400
\Bibitem{Sha15}
\by M.~V.~Shamolin
\paper Rigid body motion in a resisting medium modelling and analogues with vortex streets
\jour Mat. Model.
\yr 2015
\vol 27
\issue 1
\pages 33--53
\mathnet{http://mi.mathnet.ru/mm3562}
\elib{https://elibrary.ru/item.asp?id=23421462}
\transl
\jour Math. Models Comput. Simul.
\yr 2015
\vol 7
\issue 4
\pages 389--400
\crossref{https://doi.org/10.1134/S2070048215040092}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84937782358}
Linking options:
https://www.mathnet.ru/eng/mm3562
https://www.mathnet.ru/eng/mm/v27/i1/p33
This publication is cited in the following 10 articles:
M. V. Shamolin, “Semeistva portretov klassov dinamicheskikh sistem mayatnikovogo tipa”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 202, VINITI RAN, M., 2021, 70–98
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, “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, “Dvizhenie tverdogo tela s perednim konusom v soprotivlyayuscheisya srede: kachestvennyi analiz i integriruemost”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 83–108
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, “Examples of Integrable Systems with Dissipation on the Tangent Bundles of Three-Dimensional Manifolds”, J. Math. Sci. (N. Y.), 250:6 (2020), 964–972
M. V. Shamolin, “Problems of Qualitative Analysis in the Spatial Dynamics of Rigid Bodies Interacting with Media”, J. Math. Sci. (N. Y.), 250:6 (2020), 984–996
M. V. Shamolin, “On the problem of free deceleration of a rigid body with the cone front part in a resisting medium”, Math. Models Comput. Simul., 9:2 (2017), 232–247
M. V. Shamolin, “Integrable motions of a pendulum in a two-dimensional plane”, Journal of Mathematical Sciences, 227:4 (2017), 419–441
Shamolin M.V., “Complete List of the First Integrals of Dynamic Equations of a Multidimensional Solid in a Nonconservative Field Under the Assumption of Linear Damping”, Dokl. Phys., 60:10 (2015), 471–475
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