Skip to main content

Classical and non-classical dynamics with constraints

  • Conference paper
  • First Online:
Global Analysis — Studies and Applications I

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1108))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Vershik A.M., Faddeev L.D. Differential geometry and Lagrangian mechanics with constraints.-Dokl. Akad. Nauk SSSR 202:3 (1972), 555–557 = Soviet Physics Doklady 17:1 (1972), 34–36.

    MATH  Google Scholar 

  2. Vershik A.M., Faddeev L.D. Lagrangian mechanics in invariant form.-In: Problems of Theoretical Physics. vol.2, Leningrad, 1975 = Selecta Math. Sov. 1:4 (1981), 339–350.

    MATH  Google Scholar 

  3. Godbillon C. Géométrie différentielle et méchanique analytique. Hermann, Paris, 1969.

    MATH  Google Scholar 

  4. Arnold V.I. Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1980.

    Google Scholar 

  5. Vershik A.M. Several remarks on infinite-dimensional problems of linear programming.-Usp. Mat. Nauk 25:5 (1970), 117–124.

    MathSciNet  MATH  Google Scholar 

  6. Vershik A.M., Chernjakov A.G. Fields of convex polytops and Pareto-Smale optimum.-In: Optimization, Novosibirsk, 1982. (To be publish in Selecta Mathematica Sovietica).

    Google Scholar 

  7. Chaplygin S.A. Studies on Dynamics of Non-Holonomic Systems, Moscow, 1949 (in Russian).

    Google Scholar 

  8. Dobronravov V.V. Foundations of Mechanics of Non-Holonomic Systems, Moscow, 1970 (in Russian).

    Google Scholar 

  9. Neimark I.I., Fufaev N.A. Dynamics of Non-Holonomic Systems, Moscow, 1967 (in Russian).

    Google Scholar 

  10. Gohman A.V. Differential-Geometric Foundations of the Classical Dynamics of Systems, Saratov, 1969 (in Russian).

    Google Scholar 

  11. Ter-Krikorov A.M. Optimal Control and Mathematical Economics, Moscow, 1977 (in Russian).

    Google Scholar 

  12. Novikov S.P. Variational methods and periodic solutions of the Kirchhoff type equations.-Funct. Anal. Appl. 15:4 (1981).

    Google Scholar 

  13. Kobayashi S., Nomizu K. Foundations of Differential Geometry, vol. 1, Interscience, New York, 1963.

    MATH  Google Scholar 

  14. Busemann H. The Geometry of Geodesics, Academic Press, New York, 1955.

    MATH  Google Scholar 

  15. Manakov S.V. Remarks on integrating the Euler equations of dynamics of n-dimensional rigid body.-Funct. Anal. Appl. 10:4(1976)

    Google Scholar 

  16. Mistchenko A.S., Fomenko A.T. Generalized Liouville's method of integrating Hamiltonian systems.-Funct. Anal. Appl. 12:2 (1978).

    Google Scholar 

  17. Alekseev V.M., Tihomirov V.M., Fomin S.V. Optimal Control, Moscow, 1981 (in Russian).

    Google Scholar 

  18. Bishop R.L., Crittenden R.J. Geometry of Manofolds, Academic Press, New York, 1964.

    MATH  Google Scholar 

  19. Stenberg S. Lectures on differental geometry. N.J., 1964.

    Google Scholar 

  20. Perelomov A. Integrable systems of classical mechanic and Lie algebras. Systems with constraints. ITEP-116, preprint, Moscow, 1983 (in Russian).

    Google Scholar 

  21. Gershkovich V. Twoside estimations of a metric which generated by absolutely nonholonomic distribution on a Riemanian manifold. Soviet Doklady, 1984.

    Google Scholar 

  22. Vershik A., Chernjakov A. Critical points of fields of convex polytopes and the Pareto-Smale optimum with respect to a convex cone. Soviet Math. Dokl. Vol. 26 (1982), No.2.

    Google Scholar 

  23. Gliklikh Yu. Riemanian parallel translation in nonlinear mechanics. See this volume.

    Google Scholar 

  24. Smirnov V. A course of higher mathematics. Vol. IV, p.1, Moscow, 1974 (in Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Yurii G. Borisovich Yurii E. Gliklikh A. M. Vershik

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Vershik, A.M. (1984). Classical and non-classical dynamics with constraints. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis — Studies and Applications I. Lecture Notes in Mathematics, vol 1108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099563

Download citation

  • DOI: https://doi.org/10.1007/BFb0099563

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13910-2

  • Online ISBN: 978-3-540-39132-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics