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Classical Relativistic Extension of Kanai's Frictional Lagrangian

  • Dubey, Ritesh Kumar (Department of Physics, Banaras Hindu University) ;
  • Singh, B.K. (Department of Physics, Banaras Hindu University)
  • 투고 : 2018.04.25
  • 심사 : 2018.08.14
  • 발행 : 2018.12.30

초록

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 ${\tau}$ and the covariant velocity $u_{\mu}$ are recapitulated. Next, using a scalar function ${\psi}(x)$ and its negative derivatives ${\varphi}_{\mu}{^{\prime}}s$, we construct a covariant Lagrangian ${\Lambda}$ that generalizes the famous Bateman-Caldirola-Kanai Lagrangian of nonrelativistic frictional mechanics. Finally, we propose a deterministic model for ${\psi}$ (involving the drag coefficient A) whose explicit solution leads to relativistic damped Rayleigh motion in the rest frame of the medium.

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참고문헌

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