Skip to main content
Log in

Linear Invariant Relations in the Problem of the Motion of a Bundle of Two Bodies

  • MECHANICS
  • Published:
Doklady Physics Aims and scope Submit manuscript

Abstract

The problem of the free motion of two bodies connected by a pair of spherical hinges is considered. The conditions for the existence of invariant relations analogous to the Hess integral are specified.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

RERERENCES

  1. N. E. Zhukovskii, Zhurn. Russkogo Fiz.-Khim. Ob-va 17, 231 (1885).

    Google Scholar 

  2. V. Volterra, Acta Math. 22, 201 (1899).

    Article  MathSciNet  Google Scholar 

  3. W. Hess, Mathematische Annalen 37 (2), 153 (1890).

    Article  MathSciNet  Google Scholar 

  4. G. V. Gorr and V. N. Rubanovskii, Prikl. Mat. Mekh. 52, 707 (1988).

    Google Scholar 

  5. A. A. Burov, Izv. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 84 (1987).

    Google Scholar 

  6. E. A. Ivin, Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., No. 2, 63 (1986).

  7. V. Dragović and B. Gagić, Proc. Roy. Soc. Edinburgh, Sect. A 131 (4), 845 (2001).

    Google Scholar 

  8. A. V. Belyaev, Ukr. Matem. Vestn. 2 (33), 297 (2005).

    Google Scholar 

  9. A. V. Belyaev, Matem. Sb. 206 (5), 5 (2015).

    Article  Google Scholar 

  10. I. A. Bizyaev, A. V. Borisov, and I. S. Mamaev, Nelineinaya Dinamika 13 (3), 433 (2017).

    Article  Google Scholar 

  11. V. V. Kozlov and D. A. Onishchenko, Dokl. Akad. Nauk SSSR 266 (6), 1298 (1982).

    MathSciNet  Google Scholar 

  12. S. A. Dovbysh, Prikl. Mat. Mekh. 56 (4), 632 (1992).

    MathSciNet  Google Scholar 

  13. H. Żołądek, J. Geom. Phys. 142, 121 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  14. I. A. Bizyaev, A. V. Borisov, and I. S. Mamaev, Tr. MIAN 294, 268 (2016).

    Article  Google Scholar 

  15. A. Burov, A. Guerman, and V. Nikonov, Regular Chaotic Dyn. 25 (1), 121 (2020).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Burov.

Additional information

Translated by E. Chernokozhin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Burov, A.A. Linear Invariant Relations in the Problem of the Motion of a Bundle of Two Bodies. Dokl. Phys. 65, 147–148 (2020). https://doi.org/10.1134/S1028335820040035

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1028335820040035

Keywords:

Navigation