Skip to main content
SpringerLink
Log in

Particular solutions of the Hamilton–Jacobi equation and their usage

  • Ordinary Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We show the possibility of using particular solutions of the Hamilton–Jacobi equation in problems of qualitative analysis of Lagrangian systems with cyclic first integrals. We present a procedure for finding and studying invariant manifolds of such systems. The efficiency of the suggested approach is illustrated by examples of the solution of specific problems.

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. Gelfand, I.V. and Fomin, V.I., Variatsionnoe ischislenie (Calculus of Variations), Moscow, 1960.

    Google Scholar 

  2. Lanczos, C., The Variational Principles of Mechanics, Toronto: University of Toronto Press, 1949. Translated under the title Variatsionnye printsipy mekhaniki, Moscow: Mir, 1965.

    MATH  Google Scholar 

  3. Arnold, V.I., Kozlov, V.V., and Neishtadt, A.I., Mathematical Aspects of Classical and Celestial Mechanics, in Itogi nauki i tekhniki. Sovr. problemy matematiki. Fund. napravleniya (Progress in Science and Technology. Current Problems in Mathematics. Fundamental Directions), Moscow: VINITI, 1985, pp. 5–303.

    Google Scholar 

  4. Lyapunov, A.M., Sobranie sochinenii (Collected Papers), Moscow: Izdat. Akad. Nauk SSSR, 1954.

    Google Scholar 

  5. Prasolov, V.V., Mnogochleny (Polynomials), Moscow, 2000.

    Google Scholar 

  6. Beletskii, V.V., O dvizhenii iskusstvennogo sputnika otnositel’no tsentra mass (On the Motion of a Satellite around the Center of Mass), Moscow, 1965.

    Google Scholar 

  7. MacMillan, W.D., Dynamics of Rigid Bodies, New York: McGraw Hill, 1936. Translated under the title Dinamika tverdogo tela, Moscow: Mir, 1951.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia

    V. D. Irtegov & T. N. Titorenko

Authors
  1. V. D. Irtegov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. N. Titorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. D. Irtegov.

Additional information

Original Russian Text © V.D. Irtegov, T.N. Titorenko, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 3, pp. 301–313.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Irtegov, V.D., Titorenko, T.N. Particular solutions of the Hamilton–Jacobi equation and their usage. Diff Equat 52, 292–305 (2016). https://doi.org/10.1134/S0012266116030046

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266116030046

Keywords

Search

Navigation