Impact Factor

    Identification of parameters of the model of toroidal body motion using experimental data

    2018, Vol. 14, no. 1, pp.  99-121

    Author(s): Vetchanin  E. V., Gladkov E. S.

    This paper is concerned with the motion of heavy toroidal bodies in a fluid. For experimental purposes, models of solid tori with a width of 3 cm and external diameters of 10 cm, 12 cm and 15 cm have been fabricated by the method of casting chemically solidifying polyurethane (density 1100 kg/m3). Tracking of the models is performed using the underwater Motion Capture system. This system includes 4 cameras, computer and specialized software. A theoretical description of the motion is given using equations incorporating the influence of inertial forces, friction and circulating motion of a fluid through the hole. Values of the model parameters are selected by means of genetic algorithms to ensure an optimal agreement between experimental and theoretical data.
    Keywords: fall through a fluid, torus, body with a hole, multiply connected body, finitedimensional model, object tracking, genetic algorithms
    Citation: Vetchanin E. V., Gladkov E. S., Identification of parameters of the model of toroidal body motion using experimental data, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  99-121

    Download File
    PDF, 1.49 Mb


    [1] Борисов А. В., Кузнецов С. П., Мамаев И. С., Тененев В. А., “Описание движения тела эллиптического сечения в вязкой несжимаемой жидкости с помощью модельных уравнений, реконструированных на основе обработки данных”, Письма в ЖТФ, 42:17 (2016), 9–19; Borisov A. V., Kuznetsov S. P., Mamaev I. S., Tenenev V. A., “Describing the motion of a body with an elliptical cross section in a viscous uncompressible fluid by model equations reconstructed from data processing”, Tech. Phys. Lett., 42:9 (2016), 886–890  crossref
    [2] Ветчанин Е. В., Кленов А. И., “Экспериментальные исследования падения винтовых тел в жидкости”, Нелинейная динамика, 13:4 (2017), 585–598  mathnet [Vetchanin E. V., Klenov A. I., “Experimental investigation of the fall of helical bodies in a fluid”, Nelin. Dinam., 13:4 (2017), 585–598 (Russian)]
    [3] Ламб Г., Гидродинамика, ОГИЗ, Москва – Ленинград, 1947, 929 с.; Lamb H., Hydrodynamics, 6th ed., Dover, New York, 1945, 768 pp.
    [4] Andersen A., Pesavento U., Wang Z. J., “Unsteady aerodynamics of fluttering and tumbling plates”, J. Fluid Mech., 541 (2005), 65–90  crossref
    [5] Heisinger L., Newton P., Kanso E., “Coins falling in water”, J. Fluid Mech., 742 (2014), 243–253  crossref
    [6] Kuznetsov S. P., “Plate falling in a fluid: Regular and chaotic dynamics of finite-dimensional models”, Regul. Chaotic Dyn., 20:3 (2015), 345–382  mathnet  crossref
    [7] Mahadevan L., Ryu W. S., Samuel A. D. T., “Tumbling cards”, Phys. Fluids, 11:1 (1999), 1–3  crossref
    [8] Pesavento U., Wang Z. J., “Falling paper: Navier – Stokes solutions, model of fluid forces, and center of mass elevation”, Phys. Rev. Lett., 93:14 (2004), 144501, 4 pp.  crossref
    [9] Savitzky A., Golay M. J. E., “Smoothing and differentiation of data by simplified least squares procedures”, Anal. Chem., 36:8 (1964), 1627–1639  crossref
    [10] Vincent L., Shambaugh W.S., Kanso E., “Holes stabilize freely falling coins”, J. Fluid Mech., 801 (2016), 250–259  crossref
    [11] Willmarth W. W., Hawk N. E., Harvey R. L., “Steady and unsteady motions and wakes of freely falling disks”, Phys. Fluids, 7:2 (1964), 197–208  crossref
    [12] Zhong H., Chen S., Lee C., “Experimental study of freely falling thin disks: Transition from planar zigzag to spiral”, Phys. Fluids, 23:1 (2011), 011702, 4 pp.  crossref

    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License