Skip to main content
SpringerLink
Log in

Vector Hamiltonians in Nambu Mechanics

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We give a generalization of the Nambu mechanics based on vector Hamiltonians theory. It is shown that any divergence-free phase flow in ℝn can be represented as a generalized Nambu mechanics with n − 1 integral invariants. For the case when the phase flow in ℝn has n − 3 or less first integrals, we introduce the Cartan concept of mechanics. As an example we give the fifth integral invariant of Euler top.

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

Access this article

Log in via an institution

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

References

  1. Nambu, Y. “Generalized Hamiltonian Dynamics”, Phys. Rev. D. 7, No. 8, 5405–5412 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  2. Shafarevich, I. R. Foundations of Algebraic Geometry (MTsNMO, Moscow, 2007) [in Russian].

    MATH  Google Scholar 

  3. Dumachev, V. N. “Phase Flows and Vector Hamiltonians”, RussianMathematics 55, No. 3, 1–7 (2011).

    MathSciNet  MATH  Google Scholar 

  4. Kozlov, V. V. Integral Invariants After Poincaréand Cartan (URSS, Moscow, 1998) [in Russian].

    Google Scholar 

  5. Dumachev, V. N. “On Exact Differential Forms”, Vestn. VGU. Ser. Fizika, Matem. 2, 73–77 (2010) [in Russian].

    MathSciNet  MATH  Google Scholar 

  6. Gorieli, A. Integrability and Singularity (RKhD, Moscow, 2006) [in Russian].

    Google Scholar 

  7. Borisov, A. V.,Mamaev, I. S. Rigid Body Dynamics (RKhD, Moscow, 2001) [in Russian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Voronezh Institute of the Ministry of Internal Affairs of Russia, pr. Patriotov 53, Voronezh, 394065, Russia

    V. N. Dumachev

Authors
  1. V. N. Dumachev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. N. Dumachev.

Additional information

Original Russian Text © V.N. Dumachev, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 2, pp. 32–38.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dumachev, V.N. Vector Hamiltonians in Nambu Mechanics. Russ Math. 62, 28–33 (2018). https://doi.org/10.3103/S1066369X18020044

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X18020044

Keywords

Search

Navigation