Related papers: Relativistic dynamics without collisions and conse…
We prove that the field equations of general relativity and other metric theories can be derived from the conservation of energy-momentum without using the assumption of least action principle. We show a new procedure for perturbative…
We show that invariance of the electric charge and relativistic kinematics lead to the transformation equations for electric field intensity and the magnetic induction.
In this paper we show how to get the Lorentz transformations from E=mc^2, the laws of conservation of energy and momentum, and the special relativity principle. To this end we first deduce the law of addition of relativistic velocities
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
Considerations on the complementary time-dependent coordinate transformations emboding Lorentz transformation (LT) show that the relativistic energy-momentum relationship, implicitly the relativistic mass and energy, do not depend on the…
An equation of motion of the mass point with internal degrees of freedom in scalar potential $U$ depending on relative coordinates and time, velocity and accelerations is obtained both for non-relativistic and relativistic case. In…
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\to X$ of…
We present a relativistic formalism inspired on the Minkowski four-vectors that also includes conservation laws such as the first law of thermodynamics. It remains close to the relativistic four-vector formalism developed for a single…
In this paper, we discuss one dimensional inelastic relativistic-collisions in the framework of the relativistic kinetic theory. In particular, we focus on the relativistic effects on time evolutions of the temperature and flow velocity…
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical…
The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the…
In relativistic dynamics, force and acceleration are no longer parallel. In this article, we revisit the relativistic motion of a particle under the action of a constant force, $\boldsymbol{f}$. \ For a two-dimensional motion, the final…
What does it mean to ``add'' velocities relativistically -- clarification of the conceptual problems, new derivations of the related formulas, and identification of the source of the non-associativity of the standard vector version of the…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…
An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The microscopic deterministic mechanism of the irreversible equilibration process in…
The Radiative Vlasov-Maxwell equations model the radiative kinetics of collisionless relativistic plasma. In them the Lorentz force is modified by the addition of radiation reaction forces. The radiation forces produce damping of particle…
We consider a scenario that involves a machine gun, the bullets it fires and a moving target, considered from the rest frame of the machine gun and from the rest frame of the target respectively. Involving the special relativity via its two…
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
Experimental particle spectra can be successfully described by power-law tailed energy distributions characteristic to canonical equilibrium distributions associated to R\'enyi's or Tsallis' entropy formula - over a wide range of energies,…
Relativistic irreversible thermodynamics is reformulated following the conventional approach proposed by Meixner in the non-relativistic case. Clear separation between mechanical and non-mechanical energy fluxes is made. The resulting…