Journal of the Korean Physical Society

, Volume 73, Issue 12, pp 1840–1844 | Cite as

Classical Relativistic Extension of Kanai’s Frictional Lagrangian

  • Ritesh Kumar Dubey
  • B. K. SinghEmail author


Working in an arbitrary Lorentz frame, we address the question of formulating the covariant variational principle for classical, single-particle, dissipative, relativistic mechanics. First, within a Minkowskian geometry, the basic properties of the proper time τ and the covariant velocity uμ are recapitulated. Next, using a scalar function ψ(x) and its negative derivatives ϕμ’s, we construct a covariant Lagrangian Λ that generalizes the famous Bateman-Caldirola-Kanai Lagrangian of nonrelativistic frictional mechanics. Finally, we propose a deterministic model for ψ (involving the drag coefficient A) whose explicit solution leads to relativistic damped Rayleigh motion in the rest frame of the medium.


Relativistic dynamics Variational principle Kanai Lagrangian Drag coefficient Rayleigh motion 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. Goldstein, Classical Mechanics (Addison-Wesley/Narosa, New Delhi, 1985).zbMATHGoogle Scholar
  2. [2]
    H. C. Corben and P. Stehle, Classical Mechanics (Wiley, New York, 1960).zbMATHGoogle Scholar
  3. [3]
    K. Kanai, Prog. Theor. Phys. 3, 440 (1948).ADSCrossRefGoogle Scholar
  4. [4]
    R. W. Hasse, Rep. Prog. Phys. 41, 1027 (1978).ADSCrossRefGoogle Scholar
  5. [5]
    Yu. O. Budaev and A. G. Karavaev, Russian Phys. Journal 38, 85 (1995).CrossRefGoogle Scholar
  6. [6]
    V. J. Menon, N. Chanana and Y. Singh, Prog. Theor. Phys. 98, 321 (1997).ADSCrossRefGoogle Scholar
  7. [7]
    J. Aharoni, Special Theory of Relativity (Oxford University Press, Oxford, 1959).zbMATHGoogle Scholar
  8. [8]
    N. A. Doughty, Lagrangain Interaction (Addison-Wesley, Reading, M A, 1990).Google Scholar
  9. [9]
    Y. Sea Huang, Am. J. Phys. 67, 142 (1999).ADSCrossRefGoogle Scholar
  10. [10]
    O. D. Johns, Am. J. Phys. 53, 982 (1985).ADSCrossRefGoogle Scholar
  11. [11]
    H. Stephani, General Relativity (Cambridge University Press, London, 1985).zbMATHGoogle Scholar
  12. [12]
    G. Gonzalez, Relativistic motion with linear dissipation, arXiv:quant-ph/0503211.Google Scholar

Copyright information

© The Korean Physical Society 2018

Authors and Affiliations

  1. 1.Department of PhysicsBanaras Hindu UniversityVaranasiIndia
  2. 2.Department of Physics, SGRPG College, DobhiPurvanchal UniversityJaunpurIndia
  3. 3.Department of PhysicsGLA UniversityMathuraIndia

Personalised recommendations