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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
Article
  • 3 Downloads

Abstract

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.

Keywords

Relativistic dynamics Variational principle Kanai Lagrangian Drag coefficient Rayleigh motion 

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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

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