Journal of Mathematical Sciences

, Volume 221, Issue 2, pp 260–296 | Cite as

Some Problems of Qualitative Analysis in the Modeling of the Motion of Rigid Bodies in Resistive Media

Article
  • 11 Downloads

Abstract

In this paper, we present a qualitative analysis of plane-parallel and spatial problems on the motion of realistic rigid bodies in a resistive medium and construct a nonlinear model of the influence of the medium on the rigid body.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yu. K. Bivin, “Change of direction of motion of a rigid body on separation boundary of a medium,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 105–109 (1981).Google Scholar
  2. 2.
    Yu. K. Bivin, Yu. M. Glukhov, and Yu. V. Permyakov, “Vertical entrance of rigid bodies into water,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 3–9 (1985).Google Scholar
  3. 3.
    Yu. K. Bivin, V. V. Viktorov, and L. L. Stepanov, “Study of rigid body motion in a clayey medium,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 159–165 (1978).Google Scholar
  4. 4.
    G. S. Byushgens and R. V. Studnev, Dynamics of Longitudinal and Lateral Motion [in Russian], Mashinostroenie, Moscow (1969).Google Scholar
  5. 5.
    G. S. Byushgens and R. V. Studnev, Airplane Dynamics. Spatial Motion [in Russian], Mashinostroenie, Moscow (1988).Google Scholar
  6. 6.
    S. A. Chaplygin, “On motion of heavy bodies in an incompressible fluid,” in: A Complete Collection of Works [in Russian], Vol. 1, Izd. Akad. Nauk SSSR, Leningrad (1933), pp. 133–135.Google Scholar
  7. 7.
    S. A. Chaplygin, Selected Works [in Russian], Nauka, Moscow (1976).Google Scholar
  8. 8.
    V. A. Eroshin, “Ricochet of a lamina from the surface of an ideal incompressible fluid,” Vestn. MGU, Ser. 1., Mat., Mekh., No. 6, 99–104 (1970).Google Scholar
  9. 9.
    V. A. Eroshin, “Immersion of a disk into a compressible fluid at an angle to a free surface,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 2, 142–144 (1983).Google Scholar
  10. 10.
    V. A. Eroshin, G. A. Konstantinov, N. I. Romanenkov, and Yu. L. Yakimov, “Experimental finding of the pressure on a disk under its immersion into a compressible fluid at an angle to a free surface,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 21–25 (1988).Google Scholar
  11. 11.
    V. A. Eroshin, G. A. Konstantinov, N. I. Romanenkov, and Yu. L. Yakimov, “Experimental finding of hydrodynamical force moment under an asymmetric penetration of a disk into a compressible fluid,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, 5, 88–94 (1990).Google Scholar
  12. 12.
    V. A. Eroshin, V. A. Privalov, and V. A. Samsonov, “Two model problems of body motion in a resistive medium,” in: Collection of Scientific-Methodological Papers in Theoretical Mechanics [in Russian], Issue 18, Nauka, Moscow (1987), pp. 75–78.Google Scholar
  13. 13.
    V. A. Eroshin, N. I. Romanenkov, I. V. Serebryakov, and Yu. L. Yakimov, “Hydrodynamical forces under a shock of blunt bodies on compressible fluid surface, Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, 6, 44–51 (1980).Google Scholar
  14. 14.
    V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin, “On the motion of a body under streamline flow,” in: Abstracts of All-Union Conference on Stability of Motion, Oscillations of Mechanical Systems, and Aerodynamics, Moscow, February 2–4, 1988 [in Russian], Moscow Aviation Institute, Moscow (1988), p. 21.Google Scholar
  15. 15.
    V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin, “Mathematical modelling in problem of body drag in a medium under streamline flow,” in: Abstracts of Chebyshev Readings, Vestn. MGU, Ser. 1, Mat., Mekh., 6 (1995), p. 17.Google Scholar
  16. 16.
    V. A. Eroshin, V. A. Samsonov, and M. V. Shamolin, “Model problem of body drag in a resistive medium under streamline flow,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, 3, 23–27 (1995).Google Scholar
  17. 17.
    D. V. Georgievskii and M. V. Shamolin, “Valerii Vladimirovich Trofimov,” in: J. Math. Sci., 154, No. 4, 449–461 (2008).Google Scholar
  18. 18.
    M. I. Gurevich, Jet Theory of Ideal Fluid [in Russian], Nauka, Moscow (1979).Google Scholar
  19. 19.
    G. Lamb, Hydrodynamics [Russian translation], Fizmatgiz, Moscow (1947).MATHGoogle Scholar
  20. 20.
    B. Ya. Lokshin, V. A. Privalov, and V. A. Samsonov, Introduction to the Problem on the Motion of a Body in a Resistive Medium [in Russian], Moscow (1986).Google Scholar
  21. 21.
    H. Poincaré, On Curves Defined by Differential Equations [Russian translation], OGIZ, Moscow–Leningrad (1947).MATHGoogle Scholar
  22. 22.
    L. Prandtl and A. Betz, Ergebmisse der Aerodinamischen Versuchsastalt zu Gottingen, Berlin (1932).Google Scholar
  23. 23.
    V. A. Samsonov, V. A. Eroshin, G. A. Konstantinov, and V. M. Makarshin, “Two model problems on the motion of a body in a medium under streamline flow,” in: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 3427, Institute of Mechanics, Moscow State University, Moscow (1987).Google Scholar
  24. 24.
    V. A. Samsonov and M. V. Shamolin, “Problem of the motion of a body in a resistive medium,” Vestn. MGU, Ser. 1, Mat., Mekh., 3, 51–54 (1989).Google Scholar
  25. 25.
    V. A. Samsonov and M. V. Shamolin, “On the motion of a body in a resistive medium,” in: Contemporary Problems of Mechanics and Technologies of Machine Industry, All-Union Conference, April, 16–18, 1989. Abstracts of Reports [in Russian], All-Union Institute for Scientific and Technical Information, Moscow (1989), pp. 128–129.Google Scholar
  26. 26.
    V. A. Samsonov and M. V. Shamolin, “A model problem of the motion of a body in a medium with streamline flow,” Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 3969, Institute of Mechanics, Moscow State University, Moscow (1990).Google Scholar
  27. 27.
    V. A. Samsonov and M. V. Shamolin, “A model problem of the motion of a body in a medium with streamline flow,” in: Nonlinear Oscillations of Mechanical Systems, Abstract of Reports of II All-Union Conference, September, 1990 [in Russian], Pt. 2, Gor’kii (1990), pp. 95–96.Google Scholar
  28. 28.
    V. A. Samsonov and M. V. Shamolin, “Problem of body drag in a medium under streamline flow,” in: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 4141, Institute of Mechanics, Moscow State University, Moscow (1991).Google Scholar
  29. 29.
    V. A. Samsonov, M. V. Shamolin, V. A. Eroshin, and V. M. Makarshin, “Mathematical modelling in problem of body drag in a resistive medium under streamline flow,” in: Scientific Report of Institute of Mechanics, Moscow State University [in Russian], No. 4396, Moscow (1995).Google Scholar
  30. 30.
    L. I. Sedov, Mechanics of Continuous Media [in Russian], Vols. 1, 2, Nauka, Moscow (1983–1984).Google Scholar
  31. 31.
    M. V. Shamolin, “Problem of the motion of a body in a medium with resistance,” Vestn. MGU, Ser. 1, Mat., Mekh., 1, 52–58 (1992).Google Scholar
  32. 32.
    M. V. Shamolin, “Classification of phase portraits in the problem of the motion of a body in a resistive medium under presence of a linear damping moment,” Prikl. Mat. Mekh., 57, No. 4, 40–49 (1993).MathSciNetGoogle Scholar
  33. 33.
    M. V. Shamolin, “A new two-parameter family of phase portraits in problem of the motion of a a body in a medium,” Dokl. Ross. Akad. Nauk, 337, No. 5, 611–614 (1994).MathSciNetGoogle Scholar
  34. 34.
    M. V. Shamolin, “Introduction to problem of body drag in a resistive medium and a new twoparameter family of phase portraits, ” Vestn. MGU, Ser. 1, Mat., Mekh., 4, 57–69 (1996).Google Scholar
  35. 35.
    M. V. Shamolin, “Introduction to spatial dynamics of rigid body motion in a resistive medium,” in: Materials of International Conference and Chebyshev Readings Devoted to the 175th Anniversary of P. L. Chebyshev, Moscow, May 14–19, 1996, Vol. 2 [in Russian], MGU, Moscow (1996), pp. 371–373.Google Scholar
  36. 36.
    M. V. Shamolin, “Variety of types of phase portraits in dynamics of a rigid body interacting with a resistive medium,” Dokl. Ross. Akad. Nauk, 349, No. 2, 193–197.Google Scholar
  37. 37.
    M. V. Shamolin, “Periodic and Poisson stable trajectories in problem of the motion of a body in a resistive medium,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 2, 55–63 (1996).Google Scholar
  38. 38.
    M. V. Shamolin, “Mathematical modelling of dynamics of a spatial pendulum in a flow of a medium,” in: Proc. VII Int. Symp. ‘Methods of Discrete Singularities in Problems of Mathematical Physics,’ June 26–29, Feodociya [in Russian], Kherson State Technical University, Kherson (1997), pp. 153–154.Google Scholar
  39. 39.
    M. V. Shamolin, “Spatial dynamics of a rigid body interacting with a medium,” in: Workshop in Mechanics of Systems and Problems of Motion Control and Navigation, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 4, 174 (1997).Google Scholar
  40. 40.
    M. V. Shamolin, “Families of portraits with limit cycles in plane dynamics of a rigid body interacting with a medium,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 6, 29–37 (1998).Google Scholar
  41. 41.
    M. V. Shamolin, “Certain classes of partial solutions in dynamics of a rigid body interacting with a medium,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 2, 178–189 (1999).Google Scholar
  42. 42.
    M. V. Shamolin, “Jacobi integrability in problem of four-dimensional rigid body motion in a resistive medium.” Dokl. Ross. Akad. Nauk, 375, No. 3, 343–346. (2000).Google Scholar
  43. 43.
    M. V. Shamolin, “A new family of phase portraits in spatial dynamics of a rigid body interacting with a medium,” Dokl. Ross. Akad. Nauk, 371, No. 4, 480–483 (2000).MathSciNetGoogle Scholar
  44. 44.
    M. V. Shamolin, “Geometric representation of motion in a certain problem of body interaction with a medium,” Prikl. Mekh., 40, No. 4, 137–144 (2004).MathSciNetMATHGoogle Scholar
  45. 45.
    M. V. Shamolin, “Problem on rigid body spatial drag in a resistive medium,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 3, 45–57 (2006).Google Scholar
  46. 46.
    M. V. Shamolin, “Model problem of the motion of a body in a resistive medium with account for dependence of resistance force on angular velocity,” in: Scientifuc Report of Institute of Mechanics, Moscow State University [in Russian], No. 4818, Institute of Mechanics, Moscow State University, Moscow (2006).Google Scholar
  47. 47.
    M. V. Shamolin, Methods for Analysis of Variable-Dissipation Dynamical Systems in Rigid Body Dynamics [in Russian], Ekzamen, Moscow (2007).MATHGoogle Scholar
  48. 48.
    M. V. Shamolin, “Some model problems of dynamics for a rigid body interacting with a medium,” Prikl. Mekh., 43, No. 10, 49–67 (2007).MathSciNetMATHGoogle Scholar
  49. 49.
    M. V. Shamolin, “Dynamical systems with variable dissipation: Approaches, methods, and applications,” Fund. Prikl. Mat., 14, No. 3, 3–237 (2008).MathSciNetGoogle Scholar
  50. 50.
    M. V. Shamolin, “Three-parameter family of phase portraits in dynamics of a solid interacting with a medium,” Dokl. Ross. Akad. Nauk, 418, No. 1, 46–51 (2008).MATHGoogle Scholar
  51. 51.
    M. V. Shamolin, “Stability of rectilinear translational motion,” Prikl. Mekh., 45, No. 6, 125–140 (2009).MATHGoogle Scholar
  52. 52.
    M. V. Shamolin, “On the problem of the motion of the body with front flat butt end in a resistive medium,” in: Scientific Report of Institute of Mechamics, Moscow State University [in Russian], No. 5052, Institute of Mechanics, Moscow State University, Moscow (2010).Google Scholar
  53. 53.
    M. V. Shamolin, “Spatial motion of a rigid body in a resistive medium,” Prikl. Mekh., 46, No. 7, 120–133 (2010).Google Scholar
  54. 54.
    M. V. Shamolin, “Rigid body motion in a resistive medium,” Mat. Model., 23, No. 12, 79–104 (2011).MathSciNetMATHGoogle Scholar
  55. 55.
    M. V. Shamolin, “A multiparameter family of phase portraits in the dynamics of a rigid body interacting with a medium,” Vestn. MGU, Ser. 1, Mat., Mekh., 3, 24–30 (2011).Google Scholar
  56. 56.
    M. V. Shamolin, “The problem of a rigid body motion in a resistive medium with the assumption of dependence of the force moment on the angular velocity,” Mat. Model., 24, No. 10, 109–132 (2012).MathSciNetMATHGoogle Scholar
  57. 57.
    M. V. Shamolin, “Some classical problems in the three-dimensional dynamics of a rigid body interacting with a medium,” in: Proc. of ICTACEM’98, Kharagpur, India, Dec.1–5, 1998, Aerospace Engineering Dep., Indian Institite of Technology, Kharagpur, India (1998), 11 p.Google Scholar
  58. 58.
    M. V. Shamolin, “Mathematical modelling of interaction of a rigid body with a medium and new cases of integrability,” in: Book of Abstracts of ECCOMAS 2000, Barcelona, Spain, 11–14 September, Barcelona (2000), p. 495.Google Scholar
  59. 59.
    M. V. Shamolin and S. V. Tsyptsyn, “Analytical and numerical study of trajectories of the motion of a body in a resistive medium,” in: Sci. Rept. Inst. Mechanics, Moscow State University [in Russian], No. 4289, Institute of Mechanics, Moscow State University, Moscow (1993).Google Scholar
  60. 60.
    V. V. Sychev, A. I. Ruban, and G. L. Korolev, Asymptotic Theory of Separation Flows [in Russian], Nauka, Moscow (1987).MATHGoogle Scholar
  61. 61.
    V. G. Tabachnikov, “Stationary characteristics of wings at small velocities under whole range of angles of attack,” in: Proceedings of Central Aero-Hydrodynamical Institute [in Russian], No. 1621, Moscow (1974), pp. 18–24.Google Scholar
  62. 62.
    V. V. Trofimov and M. V. Shamolin, “Geometrical and dynamical invariants of integrable Hamiltonian and dissipative systems,” Fundam. Prikl. Mat., 16, No. 4, 3–229 (2010).Google Scholar
  63. 63.
    Yu. G. Vyshkvarko and M. V. Shamolin, “Some problems of qualitative theory in rigid body dynamics”, in: All-Russian Conference in Honour of 110th Anniversary of Mathematics Faculty of MPSU ‘Mathematics, Informatics and Methodology of Its Teaching. Moscow, March 14–16’ [in Russian], Moscow, MPSU, pp. 40–41 (2011).Google Scholar
  64. 64.
    N. E. Zhukovskii, “On a fall of light oblong bodies rotating around their longitudinal axis,” in: A Complete Collection of Works [in Russian], Vol. 5, Fizmatgiz, Moscow (1937), pp. 72–80, 100–115.Google Scholar
  65. 65.
    N. E. Zhukovski, “On bird soaring,” in: A Complete Collection of Works [in Russian] Vol. 5, Fizmatgiz, Moscow (1937), pp. 49–59.Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institute of Mechanics of the M. V. Lomonosov Moscow State UniversityMoscowRussia

Personalised recommendations