Skip to main content
SpringerLink
Log in

Technical Stability of Dynamic States of Controlled Elastic Aircraft

  • Published:
International Applied Mechanics Aims and scope

Abstract

Sufficient conditions are obtained for the technical stability of the controlled longitudinal vertical motion of elongated elastic aircraft. These aircraft are considered to have a variable cross-section and to be subject to significant transverse deformations and vibrations. The technical-stability criteria formulated depend on a small positive parameter. This parameter is a function of key parameters of the controlled dynamic process such as the increment in the transverse load due to the curvature of the system axis and the aerodynamic forces

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. K. A. Abgaryan, “Motion stability on a finite time interval, ” in: Science and Engineering Summary. General Mechanics [in Russian], Vol. 3, VINITI, Moscow (1976), pp. 43–127.

    Google Scholar 

  2. F. D. Bairamov, “Technical stability of distributed-parameter systems under permanent perturbations, ” Izv. Vuzov, Aviats. Tekhn., Issue 2, 5–11 (1974).

  3. F. D. Bairamov, “Providing technical stability of controlled systems, ” in: Problems of Analytical Mechanics, Stability, and Motion Control [in Russian], Nauka, Novosibirsk (1991), pp. 134–144.

    Google Scholar 

  4. B. N. Bublik, F. G. Garashchenko, and N. F. Kirichenko, Structurally Parametric Optimization and Motion Stability [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  5. F. G. Garashchenko and N. F. Kirichenko, “Studying problems of practical stability and motion stabilization, ” Mekh. Tverd. Tela, No. 6, 15–24 (1975).

  6. V. M. Kuntsevich and M. M. Lychak, Lyapunov-Function Synthesis of Automatic Control Systems [in Russian], Nauka, Kiev (1977).

    Google Scholar 

  7. T. K. Sirazetdinov, Stability of Distributed-Parameter Systems [in Russian], Nauka, Novosibirsk (1987).

    Google Scholar 

  8. K. S. Matviichuk, “On the comparison method for differential almost hyperbolic equations, ” Diff. Uravn., 20, No. 11, 2009–2011 (1984).

    Google Scholar 

  9. K. S. Matviichuk, “Technical stability of parametrically excited distributed processes, ” Prikl. Mat. Mekh., 50, No. 2, 210–218 (1986).

    Google Scholar 

  10. K. S. Matviichuk, “Technical stability of motion of a panel in a gas flow, ” Zh. Prikl. Mekh. Tekhn. Fiz., No. 6(172), 93–99 (1988).

    Google Scholar 

  11. K. S. Matviichuk, “Technical theory of parametrically excited panels in a gas flow, ” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 122–131 (1990).

  12. K. S. Matviichuk, “Technical stability of the solutions of a boundary-value problem for an extended beam system moving in a liquid, ” Prikl. Mekh., 32, No. 7, 84–89 (1996).

    Google Scholar 

  13. K. S. Matviichuk, “Technical stability of controlled distributed-parameter processes, ” Probl. Upravl. Inform., No. 2, 74–81 (1998).

  14. K. S. Matviichuk, “Technical stability of the solutions of a nonlinear boundary-value problem characterizing parametrically excited processes in a Hilbert space, ” Ukr. Mat. Zh., 51, No. 3, 349–363 (1999).

    Google Scholar 

  15. A. M. Letov, The Mathematical Theory of Control Processes [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  16. T. K. Sirazetdinov, “Optimal control of an aircraft, ” Avtomat. Telemekh., No. 7, 29–36 (1966).

  17. T. K. Sirazetdinov, “On the synthesis of optimal control of an aircraft, ” Izv. Vuzov, Aviats. Tekh., No. 4, 30–40 (1967)

  18. T. K. Sirazetdinov, Optimization of Distributed-Parameter Systems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  19. K. A. Lurie, Optimal Control in Problems of Mathematical Physics [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  20. H. W. Liepmann and A. Roshko, Elements of Gasdynamics (Galcit Aeronautic Series), Wiley, New York, Chapman and Hall, London (1957).

    Google Scholar 

  21. G. G. Chernyi, High-Supersonic Gas Flow [in Russian], Fizmatgiz, Moscow (1959).

    Google Scholar 

  22. K. S. Kolesnikov, A Liquid-Propellant Rocket as a Control Object [in Russian], Mashinostroenie, Moscow (1969).

    Google Scholar 

  23. V. V. Rumyantsev, “The theory of motion of solids with cavities filled with fluids,” Prikl. Mat. Mekh., 30, No. 1, 51–66 (1966).

    Google Scholar 

  24. Yu. A. Mitropol'skii, The Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1971).

    Google Scholar 

  25. V. M. Matrosov, L. Yu. Anapol'skii, and S. N. Vasil'ev, The Comparison Method in Mathematical Systems Theory [in Russian], Nauka, Novosibirsk (1980).

    Google Scholar 

  26. J. Szarski, Differential Inequalities, PWN, Warsaw (1967).

    Google Scholar 

  27. K. S. Matviichuk, “Technical stability of discontinuous control system with a continuous set of initial perturbations, ” Int. Appl. Mech., 36, No. 11, 1520–1531 (2000).

    Google Scholar 

  28. K. V. Frolov and O. I. Kosarev, “Vibroexcitation in the meshing of imprecise deformable teeth in a spur gear: a review, ” Int. Appl. Mech., 35, No. 11, 1081–1095 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev

    K. S. Matviichuk

Authors
  1. K. S. Matviichuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Matviichuk, K.S. Technical Stability of Dynamic States of Controlled Elastic Aircraft. International Applied Mechanics 37, 550–563 (2001). https://doi.org/10.1023/A:1017932717726

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1017932717726

Keywords

Search

Navigation