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Classical Relativistic Extension of Kanai's Frictional Lagrangian
Ritesh Kumar Dubey,K. Singh 한국물리학회 2018 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.73 No.12
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 and the covariant velocity u are recapitulated. Next, using a scalar function (x) and its negative derivatives ''s, we construct a covariant Lagrangian that generalizes the famous Bateman-Caldirola-Kanai Lagrangian of non- relativistic frictional mechanics. Finally, we propose a deterministic model for (involving the drag coecient A) whose explicit solution leads to relativistic damped Rayleigh motion in the rest frame of the medium.