arXiv subjects
Publications and source records attributed to Kostadin Trencevski.
This paper is a continuation of the papers [2,3,4,5,6]. In this paper the osculating spaces of arbitrary order of a manifold embedded in Euclidean space are considered. A better estimation of their dimensions as well as the description of its basis are given.
We examine the induced spin velocity in case of the Earth. Spin velocity is induced from the conversion of a constrained spatial rotation into a spatial displacement. Its effects on Earth as a celestial body are consequences of its properties and they are examined in detail. The induced spin velocity has influence to the semiannual variation of the length of day. The annual and semiannual variation of the length of day are considered separately. The measured value in case of the semiannual variation of the length of the day is 5.44% more than the predicted, while the measured value in case of the annual variation of the length of the day is 5.36% less than the predicted.
In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it is given a model of the universe, based on the Lie groups of real and complex orthogonal 3x3 matrices in this 3+3+3-dimensional space. Special attention is dedicated for introduction and study of the space SxSR, which appears to be isomorphic to SO(3,R)xSO(3,R) or S^3xS^3. The influence of the gravitational acceleration to the spinning bodies is considered. Some important applications of these results about spinning bodies are given, which naturally lead to violation of Newton's third law in its classical formulation. The precession of the spinning axis is also considered.
In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession, i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the $n$-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order $c^{-2}$.
Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the Gravity Probe B experiment, we investigated it and solved this anomaly. Thus, we proved that if our present expression for the geodetic precession is correct, then the frame dragging should be 25% less than its predicted value.
We extend the method of Huygens' construction in a uniformly moving optical medium [Am. J. Phys. 72, 934 (2004)] to the case when the medium is dispersive in its rest frame of reference. The first-order Huygens' construction analysis of the light drag in a transversely moving dispersive slab is in agreement with the results of the experiment by Jones (1975) and with the Player-Rogers formula for the downstream deflection of the beam. The derivation purports that the original Huygens' principle remains valid in non-stationary situations if it is modified to include the relativistic effects on the secondary wavelets caused by the motion of the medium.
In this paper many classes of sets of matrices with entries in F (F=R, F=C, F=H) are introduced. Each class with the corresponding topology determines a real analytical, complex or symplectic manifold for F=R, F=C or F=H respectively. Any such family is called to be a set of canonical forms of matrices. The construction of such canonical forms of matrices is introduced inductively. First basic canonical forms are introduced, and then two operations for obtaining new canonical forms by using the old canonical forms are introduced. All such manifolds have the property that each of them can be decomposed into cells of type $F^i$.
In this paper an explanation of the Pioneer anomaly is given, using the hypothesis of the time dependent gravitational potential. The implications of this hypothesis on the planetary orbits and orbital periods are given in section 2. In sections 3 and 4 we give a detailed explanation of the Pioneer anomaly, which corresponds to the observed phenomena.
It is introduced a hypothesis that the gravitational potential in the universe changes linearly with the time. This enables to explain the Hubble red shift and the anomalous acceleration of Pioneer 10 and 11.
In the paper [4] is presented a theory which unifies the gravitation theory and the mechanical effects, which is different from the Riemannian theories like GTR. Moreover it is built in the style of the electomagnetic field theory. This paper is a continuation of [4] such that the complex variant of that theory yields to the required unification of gravitation and electromagnetism. While the gravitational field is described by a scalar potential $μ$, taking a complex value of $μ$ we obtain the unification theory. For example the electric field appears to be imaginary 3-vector field of acceleration, the magnetic field appears to be imaginary 3-vector of angular velocity and the imaginary part of a complex mass is just electric charge of the particle.