Related papers: Visualizing Rotations and Composition of Rotations…

In this paper we demonstrate that subsequent application of Lorentz transformations to the cylindrical coordinates on a rotating disk leaves the Euclidean metric invariant. Therefore, the geometry on rotating disk is the Euclidean geometry,…

Vortex solutions are topologically stable field configurations that can play an important role in condensed matter, field theory, and cosmology. We investigate vortex configuration in a 2+1 dimensional Abelian Higgs theory supplemented by…

Using the coefficients introduced by Bargmann and Moshinsky for the reduction of the su($3$) algebra of Cartesian three-dimensional oscillator multiplet states into so($3$) angular momentum submultiplets, we implement unitary rotations of…

Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…

The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler-Lagrange equation,…

A geometrical approach to the covariant formulation of the dynamics of relativistic systems is introduced. A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler-Lagrange equations of a…

Because of its apparent complexity, the discussion of Wigner rotation is usually reduced to the study of Thomas precession, which is too specific a case to allow a deep understanding of boost composition. However, by simple arguments and…

Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras has been proven a useful tool for color image processing, because it additionally contains…

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…

A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous…

We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…

This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…

It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…

We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic…

As a sequel to (Berman, 2008a), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker's metric has been employed with proper-time, in its standard applications; the…

We introduce a rotation invariant short distance cut-off in the theory of an ideal fluid in three space dimensions, by requiring momenta to take values in a sphere. This leads to an algebra of functions in position space is non-commutative.…

Equilibrium solutions are believed to structure the pathways for ergodic trajectories in a dynamical system. However, equilibria are atypical for systems with continuous symmetries, i.e. for systems with homogeneous spatial dimensions,…

We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions through the repeated application of creation operators on the constant 1. Three expressions for the creation operators are derived one from the…

This paper discusses the construction of a new $(3+1)$-dimensional Korteweg-de Vries (KdV) equation. By employing the KdV's recursion operator, we extract two equations, and with elemental computation steps, the obtained result is $…

In this paper, we consider a simple kinematic model, which is a rotating disc on the edge of another fixed disc without slipping, and study the rotation angle of the rotating disc. The rotation angle consists of two parts, the dynamical…