Invariant Sets of Mechanical Systems

  • A. V. Karapetyan
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 387)


There are discussed problems of the existence and stability of invariant sets of mechanical systems (in particular, steady motions and relative equilibria).

The existence problem of stable motions (zero-dimensional invariant sets) firstly was investigated in the [1]. Really, the famous Routh theory [1]–[15] gives stability conditions of steady motions of conservative mechanical systems with first integrals as well as construction method of such steady motions. This method was spreaded for the construction problem of steady motions not only stable [2], [7] and for dissipative system with first integrals [12]–[15].

Moreover the Routh theory was modified to the existence and stability problems of invariant sets of dynamical systems with an ungrowing function and first integrals [7], [14] (in particular, of conservative and dissipative mechanical systems with symmetry [16]–[19]).


Relative Equilibrium Steady Motion Dissipative Force Local Strict Minimum Total Mechanical Energy 
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Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • A. V. Karapetyan
    • 1
  1. 1.Russian Academy of SciencesMoscowRussia

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