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Generalized Smale Diagrams for Dissipative Systems with Symmetry

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Abstract—

The problem of a global qualitative analysis of the dynamics of dissipative systems with symmetry based on generalized Smale diagrams is discussed. The general statements are illustrated by the example of the problem of the motion of a spinning top with a viscous filler.

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REFERENCES

  1. S. Smale, “Topology and mechanics,” Invent. Math. 10, 305–311 (1970); 11, 45–64 (1970).

  2. A. V. Karapetyan, “First integrals, invariant sets and bifurcations in dissipative systems,” Regular Chaotic Din. 2 (1), 75–80 (1997).

    MathSciNet  MATH  Google Scholar 

  3. A. V. Karapetyan, “Invariant sets of mechanical systems,” in Modern Methods of Analytical Mechanics and their Applications (Springer, Wien, New York, 1998), pp. 153–210.

    Google Scholar 

  4. A. V. Karapetyan, Stability and Bifurcation of Movements (MSU, Moscow, 2020) [in Russian].

    Google Scholar 

  5. N. N. Moiseev and V. V. Rumyantsev, Dynamics of Bodies with Cavities Containing Fluid (Nauka, Moscow, 1965) [in Russian].

    MATH  Google Scholar 

  6. A. V. Karapetyan, V. A. Samsonov, and T. S. Sumin, “The stability and branching of the permanent rotations of a rigid body with a fluid filling,” J. Appl. Math. Mech. 68 (6), 893–897 (2004).

    Article  MathSciNet  Google Scholar 

  7. A. V. Karapetyan, “Global qualitative analysis of tippe top dynamics,” Mech. Solids 43 (3), 342–348 (2008). https://doi.org/10.3103/S0025654408030059

    Article  ADS  Google Scholar 

  8. A. A. Zobova and A. V. Karapetyan, “Analysis of the steady motions of the tippe top,” J. Appl. Math. Mech. 73 (6), 623–630 (2009).

    Article  MathSciNet  Google Scholar 

  9. A. A. Zobova, “Various friction models in two-sphere top dynamics,” Mech. Solids 48 (2), 134–139 (2013). https://doi.org/10.3103/S0025654413020039

    Article  ADS  Google Scholar 

  10. A. A. Zobova, “A review of models of distributed dry friction,” J. Appl. Math. Mech. 80 (2), 141–148 (2016).

    Article  MathSciNet  Google Scholar 

  11. A. V. Karapetyan and A. A. Zobova, “Tippe-top on visco-elastic plane: steady-state motions, generalized smale diagrams and overturns,” Lobachevskii J. Math. 38 (6), 1007–1013 (2017).

    Article  MathSciNet  Google Scholar 

  12. M. A. Munitsyna, “Transition processes in tippe-top dynamics,” Mech. Solids 55, 1178–1184 (2020). https://doi.org/10.3103/S0025654420080178

    Article  ADS  Google Scholar 

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Funding

The work was supported by the Russian Foundation for Basic Research, project no. 19-01-00140.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. V. Karapetyan

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  1. A. V. Karapetyan
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Correspondence to A. V. Karapetyan.

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Translated by E. Oborin

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Karapetyan, A.V. Generalized Smale Diagrams for Dissipative Systems with Symmetry. Mech. Solids 56, 1471–1476 (2021). https://doi.org/10.3103/S0025654421080203

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  • DOI: https://doi.org/10.3103/S0025654421080203

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