Advertisement

The Theory of Flight

  • Genady P. CherepanovEmail author
Chapter

Abstract

The basic equations of gas dynamics are written in the form of invariant integrals describing the laws of conservation. The Kutta–Joukowski equation and the lift force of wings were derived from Joukowski’ profiles using the invariant integrals and complex variables. The optimal shape of airfoils is suggested and calculated. Method of discrete vortices applied to turbulent flows with large Reynolds number appeared to be useful for the characterization of hurricanes. This chapter may be of special interest for aerodynamics and meteorology.

Literature

  1. 1.
    G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, London, 1977), p. 750Google Scholar
  2. 2.
    G. Birkhoff, E.H. Zarantonello, Jets, Wakes and Cavities (Academic Press, New York, 1957), 280 ppGoogle Scholar
  3. 3.
    S.A. Chaplygin, On Gas Jets (Moscow University Press, 1902), 180 ppGoogle Scholar
  4. 4.
    G.P. Cherepanov, An introduction to singular integral equations in aerodynamics, in Method of Discrete Vortices, ed. G.P. Cherepanov, S.M. Belotserkovsky, I.K. Lifanov (CRC Press, Boca Raton, 1993), 450 ppGoogle Scholar
  5. 5.
    G.P. Cherepanov, An introduction to two-dimensional separated flows, in Two-Dimensional Separated Flows, ed. G.P. Cherepanov, S.M. Belotserkovsky, et al. (CRC Press, Boca Raton, 1993), 320 ppGoogle Scholar
  6. 6.
    G.P. Cherepanov, The solution to one linear Riemann problem. J. Appl. Math. Mech. (JAMM) 26(5), 623–632 (1962)Google Scholar
  7. 7.
    G.P. Cherepanov, The flow of an ideal fluid having a free surface in multiple connected domains. J. Appl. Math. Mech. (JAMM) 27(4), 508–514 (1963)Google Scholar
  8. 8.
    G.P. Cherepanov, On stagnant zones in front of a body moving in a fluid. J. Appl. Mech. Tech. Phys. (JAMTP) (3), 374–378 (1963)Google Scholar
  9. 9.
    G.P. Cherepanov, The Riemann-Hilbert problems of a plane with cuts. Dokl. USSR Acad. Sci. (Math.) 156(2) (1964)Google Scholar
  10. 10.
    G.P. Cherepanov, On one case of the Riemann problem for several functions. Dokl. USSR Acad. Sci. (Math.) 161(6) (1965)Google Scholar
  11. 11.
    G.P. Cherepanov, Invariant Γ-integrals and some of their applications to mechanics. J. Appl. Math. Mech. (JAMM) 41(3) (1977)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    G.P. Cherepanov, Invariant Γ-integrals. Eng. Fract. Mech. 14(1) (1981)Google Scholar
  13. 13.
    G.P. Cherepanov, Invariant integrals in continuum mechanics. Soviet Appl. Mech. 26(7) (1990)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    F.D. Gakhov, Boundary Value Problems (Pergamon Press, London, 1980)Google Scholar
  15. 15.
    M.I. Gurevich, The Theory of Jets in an Ideal Fluid (Academic Press, New York, 1965)Google Scholar
  16. 16.
    J. Hapel, H. Brenner, Low Reynolds Number Hydrodynamics (Prentice Hall, New York, 1965)Google Scholar
  17. 17.
    A.A. Khrapkov, Problems of elastic equilibrium of infinite wedge with asymmetrical cut at the vertex, solved in explicit form. J. Appl. Math. Mech. (JAMM) 35(6) (1971)Google Scholar
  18. 18.
    L.M. Milne-Thomson, Theoretical Hydrodynamics (Dover, New York, 1996)zbMATHGoogle Scholar
  19. 19.
    N.I. Muskhelishvili, Singular Integral Equations (Noordhoff, Groningen, 1946)Google Scholar
  20. 20.
    F.S. Sherman, Viscous Flow (McGraw Hill, New York, 1990)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.MiamiUSA

Personalised recommendations