Related papers: Relativistic dynamics without conservation laws
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…
Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls…
We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of…
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…
It is shown that if we can define a physical quantity with proper character in a given inertial reference frame (kinematic, dynamic, electromagnetic in its nature) which transforms when detected from a reference frame relative to which it…
Some useful kinematical relations for the absorption of a photon by a nucleus and its recoil are derived for the relativistic incident energies. These expressions provided for the relativistic kinematics of photoabsorption reactions, though…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…
We derive causal relativistic fluid dynamical equations from the relaxation model of kinetic theory as in a procedure previously applied in the case of non-relativistic rarefied gases. By treating space and time on an equal footing and…
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…
Entropic Dynamics is a framework in which dynamical laws such as those that arise in physics are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by…
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…
In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…
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 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…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
We present hydrodynamic equations with relativistic pressure and velocity in the presence of weak gravity, in a cosmological context. Previously we consistently derived special relativistic hydrodynamic equations with weak gravity in…
It is demonstrated that energy conservation allows for a straight derivation of Newtonian mechanics without an apriori definition of the concept of work. Furthermore it is shown that energy must be depicted as a function of position and…
We show that the transformation of relativistic velocities derived without using the Lorentz-Einstein transformation for the space-time coordinates of the same event and the fact that we can define the proper value of length, time interval,…
We present microscopic derivation of the relativistic hydrodynamics (RHD) equations directly from mechanics omitting derivation of kinetic equation. We derive continuity equation and energy-momentum conservation law. We also derive equation…
This lecture provides some introduction to perfect fluid dynamics within the framework of general relativity. The presentation is based on the Carter-Lichnerowicz approach. It has the advantage over the more traditional approach of leading…