Related papers: Energy, Forces, Fields and the Lorentz Force Formu…
The relativistic equations for the electromagnetic and gravitation interactions are similar: The only Lagrangian equation is the equation with Lorentz force. The potential satisfies the wave equation with the right - hand side proprtional…
We investigate the relativistic generalization of the classical St\"{o}rmer problem, which describes the motion of charged particles in a purely magnetic dipole field. By incorporating special relativistic effects, the particle dynamics is…
Our work is an approach between matter and energy. Using the famous equation E = mc^2, Einstein and the Law of Universal Gravitation of Newton, we estimate that a small amount matter converted into energy is needed to lift, using the…
The well known relation of Einstein relativistic energy for a free particle is extended to cover the total relativistic energy of a bound particle by calculating the relativistic potential energy. A non dissipative harmonic oscillator…
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in 4-velocity of the particle. The linear law leads to the vector gauge theory which could be the abelian…
We consider non-Lorentzian expansions, Galilean and Carrollian, of the Lorentz force equation in which both the particle position and the electro-magnetic field are expanded. There are two well-known limits in the case of a constant field,…
Minimizing the Action integral of a Lagrangian provides the Euler-Lagrange equation of motion in the elegant machinery of Lagrangian Mechanics. However two relations define the divergence of current and energy-momentum, and provide an…
We show a formal result of the longitudinal force acting on a moving potential. The potential can be velocity-dependent, which appears in various interesting physical systems, such as electrons in the presence of a magnetic flux-line, or…
As a serious attempt for constructing a new foundation for describing micro-entities from a causal standpoint, it was explained before in [1, 2, 3] that by unifying the concepts of information, matter and energy, each micro-entity is…
The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative…
In order to make plausible the idea that light exerts a pressure on matter, some introductory physics texts consider the force exerted by an electromagnetic wave on an electron. The argument as presented is both mathematically incorrect and…
We discuss the dynamics of a charged nonrelativistic particle in electromagnetic field of a rotating magnetized celestial body. The equations of motion of the particle are obtained and some particular solutions are found. Effective…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the…
We study the electromagnetic fields of an arbitrarily moving charged particle and the radiation reaction on the charged particle using a novel approach. We first show that the fields of an arbitrarily moving charged particle in an inertial…
Considering two static, electrically charged, elementary particles, we demonstrate a possible way of proving that all known fundamental forces in the nature are the manifestations of the single, unique interaction. We re-define the gauging…
It has been more than a century since first Lorentz and later Einstein explored relativistic events and still important consequences of that remains unclear to everybody. The present study extensively focus on Lorentz (Length) contraction…
We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and…
A charged particle which is allowed to accelerate must have relativistic behavior because it is coupled to electromagnetic radiation which propagates at the speed of light. We treat the simple steady-state situation of a charged particle…
We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential $V(r)=k r^{\epsilon}$. For zero total energy we show that the…