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Evolutional dynamics and stability of dissipative solids

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Summary

The paper deals with the comparative analysis of stability of the torque-free rotation of a rigid body and a solid with internal dissipation. It is shown that the dissipation-induced instability has a critical influence on stability of the rotating body. Lyapunov’s approach to stability is demonstrated to be very sensitive to the mechanical model under consideration. This sensitivity represents a weak side of Lyapunov’s approach and can be overcome by means of introducing the concept of the dissipative rigid body. On some examples we demonstrate as to how the dissipation in a rigid body is introduced and the equations of motion are derived. These equations allow one to study both the stability and the evolutional dynamics of the weakly damped mechanical systems.

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Authors and Affiliations

  1. State Polytechnical University of St. Petersburg, St Petersburg, Russia

    B. A. Smolnikov

  2. Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, St Petersburg, Russia

    Alexander K. Belyaev

Authors
  1. B. A. Smolnikov
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  2. Alexander K. Belyaev
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Corresponding author

Correspondence to Alexander K. Belyaev.

Additional information

Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday

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Smolnikov, B.A., Belyaev, A.K. Evolutional dynamics and stability of dissipative solids. Acta Mech 195, 365–377 (2008). https://doi.org/10.1007/s00707-007-0567-0

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  • DOI: https://doi.org/10.1007/s00707-007-0567-0

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