Skip to main content
Log in

Lie symmetries and conserved quantities of rotational relativistic systems

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The Lie symmetries and conserved quantities of the rotational relativistic holonomic and nonholonomic systems were studied. By defining the infinitestinal transformations' generators and by using the invariance of the differential equations under the infinitesimal transformations, the determining equations of Lie symmetries for the rotational relativistic mechanical systems are established. The structure equations and the forms of conserved quantities are obtained. An example to illustrate the application of the results is given.

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

References

  1. Bengtsson R, Frauendorf S. Quasiparticle spectra near the yrast line [J].Nucler Physics, 1979,A327: 139–171.

    Article  Google Scholar 

  2. Luo Shaokai, On the theory for relativistic analytical mechanics [J].Teaching Material Communication, 1987, (5): 31–34.

    Google Scholar 

  3. Luo Shaokai. Dynamical theory of relativistic nonlinear nonholonomic systems [J].Shanghai Journal of Mechanics, 1990,12(1): 67–70 (in Chinese)

    Google Scholar 

  4. Luo Shaokai. Relativistic variational principles and equations of motion high-order nonlinear nonholonomic system [A]. In:Proc ICDVC[C]. Beijing: Peking University Press, 1990, 645–652.

    Google Scholar 

  5. Luo Shaokai. Relativistic variation principles and equation of motion for variable mass controllable mechanics systems [J].Applied Mathematics and Mechanics (English Edition), 1996,17(7): 683–692.

    MathSciNet  Google Scholar 

  6. Carmeli M. Field theory onR×S 3 topology (I–II) [J].Foundations of Physics 1985,15(2): 175–185.

    Article  MathSciNet  Google Scholar 

  7. Carmeli M. The dynamics of rapidly rotating bodies [J].Foundations of Physics, 1985,15(8): 889–903.

    Article  MathSciNet  Google Scholar 

  8. Carmeli M. Field theory onR×S 3 topology (III) [J].Foundations of Physics, 1985,15(10): 1019–1029.

    Article  MathSciNet  Google Scholar 

  9. Carmeli M. Rotational relativity theory [J].International Journal of Theoretical Physics, 1986,25 (1): 89–94.

    Article  MATH  MathSciNet  Google Scholar 

  10. Luo Shaokai. The theory of relativistic analytical mechanics of the rotational systems [J].Applied Mathematics and Mechanics (English Edition), 1998,19(1): 45–58.

    MathSciNet  Google Scholar 

  11. Li Ziping.Classical and Quantum Constrained Systems and Their Symmetries [M]. Beijing: Beijing University of Industry Press, 1993, 244–351. (in Chinese)

    Google Scholar 

  12. Mei Fengxiang: Nother theory of Birkhoff system [J].Science in China Seres A, 1993,23(7): 709–717. (in Chinese)

    Google Scholar 

  13. Mei Fengxiang. Some applications of Lie groups and Lie algebra to the constrained mechanical systems [A]. In:MMM-VII [C]. Shanghai: Shanghai University Press, 1997, 32–40. (in Chinese)

    Google Scholar 

  14. Lutzky M. Dynamical symmetries and conserved quantities [J].J Phys A Math, 1979,12(7): 973–981.

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhao Yaoyu, Mei Fengxiang. About the symmetries and conserved quantities of mechanical systems [J].Advances in Mechanics, 1993,23(3): 360–372. (in Chinese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by Lin Zongchi

Foundation item: the National Natural Science Foundation of China (19972010); Natural Science Foundation of Henan Province (934060800, 984053100)

Biography: Fu Jingli (1955-)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jingli, F., Xiangwei, C. & Shaokai, L. Lie symmetries and conserved quantities of rotational relativistic systems. Appl Math Mech 21, 549–556 (2000). https://doi.org/10.1007/BF02459036

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02459036

Key words

CLC numbers

Navigation