On Stationary Sets of Euler’s Equations on so(3,1) and Their Stability

  • Valentin Irtegov
  • Tatyana Titorenko
Conference paper

DOI: 10.1007/978-3-319-02297-0_16

Volume 8136 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Irtegov V., Titorenko T. (2013) On Stationary Sets of Euler’s Equations on so(3,1) and Their Stability. In: Gerdt V.P., Koepf W., Mayr E.W., Vorozhtsov E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham

Abstract

With the use of computer algebra methods we investigate two recent found cases of integrability (in the Liouville sense) of Euler’s equations on the Lie algebra so(3,1) when the equations possess additional polynomial first integrals of degrees 3 and 6. The problems of obtaining stationary sets of the equations and investigation of their stability are considered. In addition to the sets obtained earlier [1], we have found new zero-dimensional and nonzero-dimensional stationary sets. For a number of the sets we have derived sufficient conditions of their stability and instability.

Keywords

Euler’s equations stationary sets stability 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

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