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    The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque

    2019, Vol. 15, no. 1, pp.  41-57

    Author(s): Vetchanin  E. V.

    The motion of a circular cylinder in a fluid in the presence of circulation and external periodic force and torque is studied. It is shown that for a suitable choice of the frequency of external action for motion in an ideal fluid the translational velocity components of the body undergo oscillations with increasing amplitude due to resonance. During motion in a viscous fluid no resonance arises. Explicit integration of the equations of motion has shown that the unbounded propulsion of the body in a viscous fluid is impossible in the absence of external torque. In the general case, the solution of the equations is represented in the form of a multiple series.
    Keywords: rigid body dynamics, ideal fluid, viscous fluid, propulsion in a fluid, resonance
    Citation: Vetchanin E. V., The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 1, pp.  41-57
    DOI:10.20537/nd190105


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    References

    [1] Bizyaev, I. A., Borisov, A. V., and Kuznetsov, S. P., “The Chaplygin Sleigh with Friction Moving due to Periodic Oscillations of an Internal Mass”, Nonlinear Dyn., 95:1 (2019), 699–714  crossref
    [2] Bizyaev, I. A., Borisov, A. V., and Kuznetsov, S. P., “Chaplygin Sleigh with Periodically Oscillating Internal Mass”, Europhys. Lett., 119:6 (2017), 60008, 7 pp.  crossref  mathscinet  adsnasa
    [3] Bizyaev, I. A., Borisov, A. V., and Mamaev, I. S., “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref  mathscinet  zmath  adsnasa
    [4] Borisov, A. V., Kozlov, V. V., and Mamaev, I. S., “Asymptotic Stability and Associated Problems of Dynamics of Falling Rigid Body”, Regul. Chaotic Dyn., 12:5 (2007), 531–565  crossref  mathscinet  zmath  adsnasa  elib
    [5] Borisov, A. V., Kuznetsov, S. P., Mamaev, I. S., and 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  adsnasa  elib; Pis'ma Zh. Tekh. Fiz., 42:17 (2016), 9–19 (Russian)
    [6] Borisov, A. V. and Kuznetsov, S. P., “Comparing Dynamics Initiated by an Attached Oscillating Particle for the Nonholonomic Model of a Chaplygin Sleigh and for a Model with Strong Transverse and Weak Longitudinal Viscous Friction Applied at a Fixed Point on the Body”, Regul. Chaotic Dyn., 23:7–8 (2018), 803–820  mathnet  crossref  mathscinet  zmath  adsnasa
    [7] Borisov, A. V. and Mamaev, I. S., Rigid Body Dynamics: Hamiltonian Methods, Integrability, Chaos, R&C Dynamics, Institute of Computer Science, Izhevsk, 2005, 576 pp. (Russian)  mathscinet
    [8] Borisov, A. V. and Mamaev, I. S., “On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation”, Chaos, 16:1 (2006), 013118, 7 pp.  crossref  mathscinet  zmath  adsnasa  elib
    [9] Borisov, A. V., Mamaev, I. S., and Vetchanin, E. V., “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502  mathnet  crossref  mathscinet  zmath  adsnasa
    [10] Borisov, A. V., Mamaev, I. S., and Vetchanin, E. V., “Self-Propulsion of a Smooth Body in a Viscous Fluid under Periodic Oscillations of a Rotor and Circulation”, Regul. Chaotic Dyn., 23:7–8 (2018), 850–874  mathnet  crossref  mathscinet  zmath  adsnasa
    [11] Borisov, A. V., Vetchanin, E. V., and Kilin, A. A., “Control Using Rotors of the Motion of a Triaxial Ellipsoid in a Fluid”, Math. Notes, 102:3–4 (2017), 455–464  mathnet  crossref  mathscinet  zmath  elib; Mat. Zametki, 102:4 (2017), 503–513 (Russian)  crossref  zmath
    [12] Brendelev, V. N., “On the Realization of Constraints in Nonholonomic Mechanics”, J. Appl. Math. Mech., 45:3 (1981), 351–355  crossref  mathscinet  zmath; Prikl. Mat. Mekh., 45:3 (1981), 481–487 (Russian)  mathscinet  zmath
    [13] Chaplygin, S. A., “On the Action of a Plane-Parallel Air Flow upon a Cylindrical Wing Moving within It”, The Selected Works on Wing Theory of Sergei A. Chaplygin, Garbell Research Foundation, San Francisco, 1956, 42–72  mathscinet
    [14] Chaplygin, S. A., “Von dem Drucke eines planparallelen Stromes auf untergetauchte Körper (zur Theorie der Aeroplane)”, Mat. Sb., 28:1 (1911), 120–166 (Russian)  mathnet
    [15] Childress, S., Spagnolie, S. E., and Tokieda, T., “A Bug on a Raft: Recoil Locomotion in a Viscous Fluid”, J. Fluid Mech., 669 (2011), 527–556  crossref  mathscinet  zmath  adsnasa  elib
    [16] Eldering, J., “Realizing Nonholonomic Dynamics as Limit of Friction Forces”, Regul. Chaotic Dyn., 21:4 (2016), 390–409  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    [17] Karapetyan, A. V., “On Realizing Nonholonomic Constraints by Viscous Friction Forces and Celtic Stones Stability”, J. Appl. Math. Mech., 45:1 (1981), 30–36  crossref  mathscinet  zmath; Prikl. Mat. Mekh., 45:1 (1981), 42–51 (Russian)  mathscinet  zmath
    [18] Karavaev, Yu. L., Kilin, A. A., and Klekovkin, A. V., “Experimental Investigations of the Controlled Motion of a Screwless Underwater Robot”, Regul. Chaotic Dyn., 21:7–8 (2016), 918–926  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    [19] Kilin, A. A., Klenov, A. I., and Tenenev, V. A., “Controlling the Movement of the Body Using Internal Masses in a Viscous Liquid”, Computer Research and Modeling, 10:4 (2018), 445–460 (Russian)  crossref
    [20] Kirchhoff, G., Vorlesungen über mathematische Physik: Vol. 1. Mechanik, Teubner, Leipzig, 1876
    [21] Klenov, A. I. and Kilin, A. A., “Influence of Vortex Structures on the Controlled Motion of an Above-Water Screwless Robot”, Regul. Chaotic Dyn., 21:7–8 (2016), 927–938  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    [22] Korotkin, A. I., Added Masses of Ship Structures, Fluid Mech. Appl., 88, Springer, Dordrecht, 2009  elib
    [23] Kozlov, V. V., “On the Problem of Fall of a Rigid Body in a Resisting Medium”, Mosc. Univ. Mech. Bull., 45:1 (1990), 30–36  mathscinet  zmath; Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 1990, no. 1, 79–86 (Russian)  zmath
    [24] Kozlov, V. V., “Realization of Nonintegrable Constraints in Classical Mechanics”, Sov. Phys. Dokl., 28 (1983), 735–737  mathscinet  zmath  adsnasa; Dokl. Akad. Nauk SSSR, 272:3 (1983), 550–554 (Russian)  mathnet  mathscinet  zmath
    [25] Kozlov, V. V. and Ramodanov, S. M., “The Motion of a Variable Body in an Ideal Fluid”, J. Appl. Math. Mech., 65:4 (2001), 579–587  crossref  mathscinet  zmath; Prikl. Mat. Mekh., 65:4 (2001), 592–601 (Russian)  mathscinet  zmath
    [26] Kozlov, V. V. and Onishchenko, D. A., “The Motion in a Perfect Fluid of a Body Containing a Moving Point Mass”, J. Appl. Math. Mech., 67:4 (2003), 553–564  crossref  mathscinet  zmath; Prikl. Mat. Mekh., 67:4 (2003), 620–633 (Russian)  mathscinet  zmath
    [27] Kutta, W. M., “Auftriebskräfte in strömenden Flüssigkeiten”, Illustr. aeronaut. Mitteilungen, 6 (1902), 133–135
    [28] 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  mathscinet  zmath  adsnasa  elib
    [29] Leonard, N. E., “Periodic Forcing, Dynamics and Control of Underactuated Spacecraft and Underwater Vehicles”, Proc. of the 34th IEEE Conf. on Decision and Control (New Orleans, La., Dec 1995), 3980–3985
    [30] Lighthill, M. J., “On the Squirming Motion of Nearly Spherical Deformable Bodies through Liquids at Very Small Reynolds Numbers”, Comm. Pure Appl. Math., 5:2 (1952), 109–118  crossref  mathscinet  zmath
    [31] Mamaev, I. S., Tenenev, V. A., and Vetchanin, E. V., “Dynamics of a Body with a Sharp Edge in a Viscous Fluid”, Rus. J. Nonlin. Dyn., 14:4 (2018), 473–494  mathscinet
    [32] Mamaev, I. S. and Vetchanin, E. V., “The Self-Propulsion of a Foil with a Sharp Edge in a Viscous Fluid under the Action of a Periodically Oscillating Rotor”, Regul. Chaotic Dyn., 23 (2018), 7–8, 875–886  crossref  mathscinet
    [33] Mason, R. J., Fluid Locomotion and Trajectory Planning for Shape-Changing Robots, PhD Dissertation, California Institute of Technology, Pasadena, Calif., 2003, 264 pp.
    [34] Michelin, S. and Llewellyn Smith, S. G., “An Unsteady Point Vortex Method for Coupled Fluid-Solid Problems”, Theor. Comput. Fluid Dyn., 23:2 (2009), 127–153  crossref  zmath  elib
    [35] Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O. I., Integrals and Series, v. 1, Elementary Functions, Gordon & Breach Sci. Publ., New York, 1986  mathscinet  zmath
    [36] Ramodanov, S. M. and Tenenev, V. A., “Motion of a Body with Variable Distribution of Mass in a Boundless Viscous Liquid”, Nelin. Dinam., 7:3 (2011), 635–647 (Russian)  mathnet  crossref  mathscinet
    [37] Ramodanov, S. M., Tenenev, V. A., and Treschev, D. V., “Self-Propulsion of a Body with Rigid Surface and Variable Coefficient of Lift in a Perfect Fluid”, Regul. Chaotic Dyn., 17:6 (2012), 547–558  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    [38] Tallapragada, Ph., “A Swimming Robot with an Internal Rotor As a Nonholonomic System”, Proc. of the American Control Conference (Chicago, Ill., USA, July 1–3, 2015), 657–662
    [39] Vetchanin, E. V. and Kilin, A. A., “Controlled Motion of a Rigid Body with Internal Mechanisms in an Ideal Incompressible Fluid”, Proc. Steklov Inst. Math., 295 (2016), 302–332  mathnet  crossref  mathscinet  zmath  elib; Tr. Mat. Inst. Steklova, 295 (2016), 321–351 (Russian)  mathscinet  zmath
    [40] Vetchanin, E. V. and Kilin, A. A., “Control of Body Motion in an Ideal Fluid Using the Internal Mass and the Rotor in the Presence of Circulation around the Body”, J. Dyn. Control Syst., 23:2 (2017), 435–458  crossref  mathscinet  zmath  elib
    [41] Vetchanin, E. V. and Kilin, A. A., “Control of the Motion of an Unbalanced Heavy Ellipsoid in an Ideal Fluid Using Rotors”, Nelin. Dinam., 12:4 (2016), 663–674 (Russian)  mathnet  crossref  mathscinet  zmath
    [42] Vetchanin, E. V., Kilin, A. A., and Mamaev, I. S., “Control of the Motion of a Helical Body in a Fluid Using Rotors”, Regul. Chaotic Dyn., 21:7–8 (2016), 874–884  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    [43] Vetchanin, E. V. and Mamaev, I. S., “Optimal Control of the Motion of a Helical Body in a Liquid Using Rotors”, Russ. J. Math. Phys., 24:3 (2017), 399–411  crossref  mathscinet  zmath  elib
    [44] Vetchanin, E. V., Mamaev, I. S., and Tenenev, V. A., “The Self-Propulsion of a Body with Moving Internal Masses in a Viscous Fluid”, Regul. Chaotic Dyn., 18:1–2 (2013), 100–117  mathnet  crossref  mathscinet  zmath  adsnasa  elib



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