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The de Broglie-Einstein velocity equation is derived for a relativistic particle by using the energy and momentum relations in terms of wave and matter properties. It is shown that the velocity equation is independent from the relativistic…
The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. The relative and center of mass coordinates are not separated, and choosing the…
The vector form of a Lorentz transformation which is separated with time and space parts is studied. It is necessary to introduce a new definition of the relative velocity in this transformation, which plays an important role for the…
We define `third derivative' General Relativity, by promoting the integration measure in Einstein-Hilbert action to be an arbitrary $4$-form field strength. We project out its local fluctuations by coupling it to another $4$-form field…
This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently…
After a short Historical bibliographical note, in the Starting points attention will be focused on some postulates common to classical mechanics and special relativity. Starting from these premises, in the sections The deduction of the form…
The dynamics of "dipolar particles", i.e. particles endowed with a four-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's world line, and of the…
We study eccentric equatorial orbits of a test-body around a Kerr black hole under the influence of gravitational radiation reaction. We have adopted a well established two-step approach: assuming that the particle is moving along a…
Relativistic Coulomb systems are studied in velocity space, prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space provides a method much simpler (and more elegant) than the familiar analytic solutions in…
It is proved that local Lorentz transformations for different systems cannot derive varying speed of light. Based on the special relativity principle, an invariant speed is necessarily obtained. Therefore, the exact basic principles of the…
In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate.…
It is standard lore that gravitational radiation reaction circularizes the orbits of inspiralling binary systems. But in recent papers, Loutrel et al. have argued that at late times in such inspirals, one measure of eccentricity actually…
This article reconsiders the relative-velocity-dependent approach to modeling electromagnetism that was proposed initially by Weber before data from cathode-ray-tube (CRT) experiments was available. It is shown that identifying 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 consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on…
The velocity field and the associated tangential stress corresponding to flow of a generalized second grade fluid between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time $t=0$…
We prescribe a pseudo-Newtonian vector potential for studying accretion disks around Kerr black holes. The potential is useful to study the inner properties of disk not confined to the equatorial plane where general relativistic effect is…
We suggest to solve for the motion of the two body problem in General Relativity by identifying the leading violation of conserved quantities, referred to as (relativistic) anomalies, ordered by the post-Newtonian order at which they…
Einstein's perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into…
Examination of the Einstein energy-momentum relationship suggests that simple unbound forms of matter exist in a four-dimensional Euclidean space. Position, momentum, velocity, and other vector quantities can be expressed as Euclidean…