Related papers: Vector constants of motion for time-dependent Kepl…
Unsteadiness lies at the heart of turbulent fluid dynamics, eddy formation and instabilities in flows thus making it central to both understanding and controlling fluid systems. In this work, we present an objective measure for the…
The infinite number of time-dependent linear in field and conjugated momenta invariants is derived for the scalar field using the Noether's theorem procedure.
Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations,…
Strichartz estimates for a time-decaying harmonic oscillator were proven with some assumptions of coefficients for the time-decaying harmonic potentials. The main results of this paper are to remove these assumptions and to enable us to…
For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation for the random…
The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and…
The trajectory and the orbital velocity are determined for an object moving in a gravitational system, in terms of fundamental and independent variables. In particular, considering a path on equipotential line, the elliptical orbit is…
A brief overview is given on precision determinations of values of the fundamental physical constants and the search for their variation with time by means of precision spectroscopy in the optical domain.
The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the Hyperbolic plane. First, the theory of central potentials on spaces of constant curvature is studied. All the…
In this work, we present the analytical approach to the evaluation of the conditional measure Wiener path integral. We consider the time-dependent model parameters. We find the differential equation for the variable, determining the…
Motivated by the Dirac idea that fundamental constant are dynamical variables and by conjectures on quantum structure of spacetime at small distances, we consider the possibility that Planck constant $\hbar$ is a time depending quantity,…
We derive formulae for the time variation of the gravitational ``constant'' and of the fine structure ``constant'' in various models with extra dimensions and analyze their consistency with the observational data.
This article describes a method devised for efficient evaluation of arbitrary static magnetic and electric fields in a source free region needed for long time tracking of charged particles. Field values given on the boundary of the region…
The presence of a cosmological constant, Lambda, in an action with higher powers of the curvature can produce rapidly oscillating metrics. We develop a perturbative approach for generating periodic solutions to the non-linear field…
The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular…
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…
In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles.…
We develop the analytical method of field momenta for analyzing the dynamics of optical vector solitons in photorefractive nonlinear media. First, we derive the effective evolution equations for the parameters of multi-component solitons…
In ZM theory the direction of time has a non-zero projection onto space and this projection corresponds to the local velocity relative to the observer. Classical trajectories can be obtained by following the local direction of time. The…
We begin with a scenario that involves point-like observers starting at t=0 from the origin O of an inertial reference frame. They move with all possible proper accelerations in the positive direction of the OX axis. Equipped with light…