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Change in the Character of Stability of Equilibrium in the Case of a Change in the Rigidity of a Generalize Coordinate

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Abstract

A linear mechanical system with n degrees of freedom is considered. The change in the character of stability of trivial equilibrium is studied in the case when the rigidity in one of the generalized coordinates changes. The maximum number of such alternations of a stability character is determined. An example of such a system is given in which the maximum amount of changes in the character of the stability occurs.

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REFERENCES

  1. D. R. Merkin, Gyroscopic Systems (Nauka, Moscow, 1974) [in Russian].

  2. A. A. Mailybaev and A. P. Seiranyan, Dokl. Akad. Nauk 436 (2), 188–194 (2011).

    MathSciNet  Google Scholar 

  3. F. E. Udwadia, AIAA J. 55 (9), 2853–2858 (2017). https://doi.org/10.2514/1.J056109

    Article  ADS  Google Scholar 

  4. D. Jekel and P. Hagedorn, Z. Angew. Math. Mech. 97 (9), 1128–1135 (2017). https://doi.org/10.1002/zamm.201600288

    Article  Google Scholar 

  5. M. Abdullatif, R. Mukherjee, and A. Hellum, J. Sound Vib. 413, 442–455 (2018). https://doi.org/10.1016/j.jsv.2017.09.018

  6. V. F. Zhuravlev, Izv. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 3–6 (2009).

    Google Scholar 

  7. V. A. Samsonov and Yu. D. Selyutskii, Prikl. Mat. Mekh. 83 (4), 597 (2019). https://doi.org/10.1134/S0032823519040131

    Article  Google Scholar 

  8. A. P. Golub and Yu. D. Selyutskii, Dokl. Akad. Nauk 481 (3), 254–257 (2018). https://doi.org/10.31857/S086956520001373-3

    Article  Google Scholar 

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00538.

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Authors and Affiliations

  1. Institute of Mechanics, Moscow State University, Moscow, Russia

    Yu. D. Selyutskiy

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  1. Yu. D. Selyutskiy
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Correspondence to Yu. D. Selyutskiy.

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Selyutskiy, Y.D. Change in the Character of Stability of Equilibrium in the Case of a Change in the Rigidity of a Generalize Coordinate. Dokl. Phys. 65, 109–111 (2020). https://doi.org/10.1134/S1028335820030131

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  • DOI: https://doi.org/10.1134/S1028335820030131

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