Related papers: Preliminary Energy Considerations in a Relativisti…
Classical non-relativistic mechanics in a general setting of time-dependent transformations and reference frame changes is formulated in the terms of fibre bundles over the time-axis R. Connections on fibre bundles are the main ingredient…
Motivated by the instability of suspension bridges, we consider a class of second order Hamiltonian systems where one component initially holds almost all the energy of the system. We show that if the total energy is sufficiently small then…
We revisit the classical theory of a relativistic massless charged point particle with spin and interacting with an external electromagnetic field. In particular, we give a proper definition of its kinetic energy and its total energy, the…
Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…
In order to describe the velocity of two bodies after they collide, Newton developed a phenomenological equation known as "Newton\' s Experimental Law" (NEL). In this way, he was able to practically bypass the complication involving the…
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
We study a system of interacting particles in the presence of the relativistic kinetic energy, external confining potentials, singular repulsive forces as well as a random perturbation through an additive white noise. In comparison with the…
The problem of energy and its localization in general relativity is critically re-examined. The Tolman energy integral for the Eddington spinning rod is analyzed in detail and evaluated apart from a single term. It is shown that a higher…
Physical systems transition between states with finite speed that is limited by energetic costs. In this work, we derive bounds on transition times for general Langevin systems that admit a decomposition into reversible and irreversible…
We apply the principle of energy conservation to the motion of the test particle in gravitational field by requiring that its energy, gained by gravitation, has to be balanced by decrease of its rest mass. Due to the change of mass in…
A new approach to the electroweak properties of two-particle composite systems is developed. The approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The main novel feature of this approach is the new…
We apply a simple decomposition to the energy of a moving particle. Based on this decomposition, we identify the potential and kinetic energies, then use them to give general definitions of momentum and the various kinds of forces exerted…
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…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
The physical consequences of the relativistic and nonrelativistic approaches to describe the energy levels of electrons which propagate in a static homogeneous magnetic field are considered. It is shown that for a given strength of the…
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to…
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the…
We derive the radiation reaction by taking into account that the acceleration of the charge is caused by the interaction with some heavy source particle. In the non relativistic case this leads, in contrast to the usual approach,…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
For the first time, using nonrelativistic approach we have calculated the attraction force, friction torque and the rate of radiation heat exchange in the system of two sprerical rotating particles located at a distance between one another.