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On Invariant Manifolds of Lagrange Systems

  • Valentin Irtegov
  • Tatyana Titorenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)

Abstract

This paper is a continuation of the previous work [1]. In the present paper we propose a new approach for obtaining and qualitative analysis of invariant manifolds of Lagrange systems, which possess cyclic first integrals. The main idea consists in the use of “extended” characteristic functions. The proposed approach is demonstrated by examples of concrete mechanical systems. The computer algebra system (CAS) “Mathematica” is applied for computations.

Keywords

Invariant Manifold Computer Algebra System Full Derivative Legendre Transformation Lagrange System 
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References

  1. 1.
    Irtegov, V.D., Titorenko, T.N.: On Reduction of Lagrange Systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2010. LNCS, vol. 6244, pp. 123–133. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Gelfand, I.M., Fomin, S.V.: Variational Calculus. GIF-ML, Moscow (1961)Google Scholar
  3. 3.
    Stekloff, V.A.: Remarque sur un problème de Clebsch sur le mouvement d‘un corps solide dans un liquide indefini et sur le problème de M. Brun. Comptes Rend. VCXXXV, 526–528 (1902)Google Scholar
  4. 4.
    Appel, P.: Traité de Mécanique Rationnelle, vol. 2. Gauthier–Villars, Paris (1953)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Valentin Irtegov
    • 1
  • Tatyana Titorenko
    • 1
  1. 1.Institute for System Dynamics and Control Theory SB RASIrkutskRussia

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