Skip to main content
SpringerLink
Log in

Mei symmetry of discrete mechanico-electrical systems

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Mei symmetry of discrete mechanico-electrical systems on a uniform lattice is investigated. The definition and criterion of the discrete analog of Mei symmetry for the system are presented. The condition of existence of the discrete Mei conserved quantity induced directly by Mei symmetry as well as its form is given. Finally, an example is discussed to illustrate these results.

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. Noether A.E.: Invariante Variationsprobleme. Nachr. Akad. Wiss. Gottingen Math. Phys. 2, 235–257 (1918)

    Google Scholar 

  2. Lutzky M.: Dynamical symmetries and conserved quantities. J. Phys. A: Math. Gen. 12, 973–981 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  3. Mei F.X.: Form invariance of Appell equations. Chin. Phys. 10, 177–180 (2001)

    Article  Google Scholar 

  4. Fang J.H.: Mei symmetry and Lie symmetry of the rotational relativistic variable mass system. Commun. Theor. Phys. 40, 269–272 (2003)

    MATH  Google Scholar 

  5. Cai J.L.: Conformal invariance and conserved quantities of general holonomic systems. Chin. Phys. Lett. 25, 1523–1526 (2008)

    Article  Google Scholar 

  6. Mei, F.X.: Symmetries and Conserved Quantities of Constrained Mechanical Systems. Beijing Institute of Technology Press, Beijing (2004) (in Chinese)

  7. Luo, S.K., Zhang, Y.F., et al.: Advances in the Study of Dynamics of Constrained Mechanics Systems. Science Press, Beijing (2008) (in Chinese)

  8. Dorodnitsyn V.: Noether-type theorems for difference equations. Appl. Numer. Math. 39, 307–321 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Fu J.L., Chen L.Q.: On Noether symmetries and form invariance of mechanico-electrical systems. Phys. Lett. A. 331, 138–152 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fu J.L., Chen L.Q., Jimnez S., Tang Y.F.: Non-Noether symmetries and Lutzky conserved quantities for mechanico- electrical systems. Phys. Lett. A. 358, 5–10 (2006)

    Article  MATH  Google Scholar 

  11. Fu J.L., Wang X.J., Xie F.P.: Conserved quantities and conformal mechanico-electrical systems. Chin. Phys. Lett. 25, 2413–2416 (2008)

    Article  Google Scholar 

  12. Fu J.L., Chen B.Y., Chen L.Q.: Noether symmetries of discrete nonholonomic dynamical systems. Phys. Lett. A. 373, 409–412 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fu J.L., Chen L.Q., Chen B.Y.: Noether-type theory for discrete mechanico-electrical dynamical systems with nonregular lattices. Sci. China Phys. Mech. Astron. 53, 1687–1698 (2010)

    Article  Google Scholar 

  14. Fu J.L., Fu H., Liu R.W.: Hojman conserved quantities of discrete mechanico-electrical systems constructed by continuous symmetries. Phys. Lett. A. 374, 1812–1818 (2010)

    Article  MathSciNet  Google Scholar 

  15. Wang P.: Perturbation to Noether symmetry and Noether adiabatic invariants of discrete mechanico-electrical systems. Chin. Phys. Lett. 28, 040203 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Purple Mountain Observatory, Chinese Academy Sciences, Nanjing, 210008, China

    M. J. Zhang

  2. Key Laboratory of Space Object and Debris Observation, PMO, CAS, Nanjing, China

    M. J. Zhang

Authors
  1. M. J. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. J. Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, M.J. Mei symmetry of discrete mechanico-electrical systems. Acta Mech 223, 679–683 (2012). https://doi.org/10.1007/s00707-011-0590-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-011-0590-z

Keywords

Search

Navigation