Uniform Translational Motion Research Articles

Relativistic light clocks: Arbitrary orientation in uniform motion and hyperbolic motion analysis

In this paper, we address the general case of a light clock in uniform translational motion parallel to itself and perpendicular to its uniform velocity v, as well as the case of the light clock in relativistic hyperbolic motion. Neither case has been previously addressed in the specialized literature, which typically restricts itself to canonical orientations where the light clock moves parallel to either the vertical or horizontal axis with uniform velocity, without acceleration. Therefore, it becomes interesting to study the more general case where the clock has an arbitrary orientation and/or is accelerated. Our paper is divided into two main sections. The first section deals with the light clock moving with constant velocity, oriented at an arbitrary angle with respect to the x-axis. We prove that the moving clock exhibits a standard time dilation, identical to that of a light clock moving in a canonical orientation. The second section deals with the light clock moving with constant acceleration, i.e., in hyperbolic motion. For the light clock in hyperbolic motion, we derive the period as measured from the perspective of an inertial frame and draw parallels with the case of uniform motion, outlining a term that is similar (but not identical) to the γ factor of uniform motion. We also point out that this factor depends not only on acceleration but also on the height of the light clock. This dependency on the dimension of the light clock distinguishes the accelerated case from the case of uniform motion. The first three sections deal with the theoretical aspects of light (optical) clocks, while the fourth section addresses the experimental implementations of optical clocks.

Mathematical model of a lightweight three-axle off-road vehicle construction for Arctic zone of Russia

Introduction. The model and results of calculating the smoothness of a light three-axle off-road vehicle for the Arctic zone of Russia are considered. The model on standard approaches and uses a system of assumptions that limits the number of degrees of freedom for the vehicle body to three, as well as one degree of freedom for the unsprung masses is based. The mathematical model is a system of ordinary differential equations and is supplemented with the necessary algebraic equations, as well as initial conditions. The system is integrated using the 4th order RungeKutta method, for which a program was written in C++. The calculations presented in the article demonstrate the possibility of conducting research on the smoothness of a vehicle under conditions of arbitrary terrain, typical for off-road conditions in the winter conditions of the Arctic zone. The dimensions and other parameters of the vehicle were taken from a full-scale model that was used in real expeditions in 2003-2019. Based on the model, suspension characteristics will be developed for a new all-terrain vehicle.Theory. When operating a wheeled vehicle in a wide range of conditions, even in northern regions, transverseangular vibrations are very often insignificant, so only vertical linear and longitudinal-angular vibrations of the frame can be considered. This problem enables to construct a system of equations of vehicle motion using selected degrees of freedom. From a mathematical point of view, these equations are classified as second-order ordinary differential equations with a variable structure of the right-hand sides, which reflects the non-linear nature of the behavior of the suspension in terms of its geometric constraints.Methods. The work uses numerical methods to solve the equations of the constructed model, which enables to gradually weaken the accepted assumptions and build more general calculation algorithms. The main integration method for ensuring the stability of solutions is the multi-step Adams method, which, with the correct choice of step, ensures the necessary stability of the solution over sufficiently long model times. However, in this work, the 4th order Runge-Kutta method was adopted, which turned out to be quite sufficient.Results and conclusions. The paper presents the results of a numerical study of the oscillatory processes of an off-road vehicle during uniform translational motion of the vehicle on a horizontal surface with a given profile of irregularities. The graphs show a transition process of oscillations, which ends with reaching a steady state. The shape of oscillations in a steady state can be irregular and significantly depends on the given speed of the all-terrain vehicle. Analysis of the dependencies presented in the figures shows that the shape of the oscillations of the allterrain vehicle’s frame, as well as the amplitude and frequency, significantly depend on the speed of the vehicle (at a constant road profile). Changing the road profile leads to corresponding changes in the forms and characteristics of forced vibrations of a vehicle on a suspension, which makes it possible to build the necessary amplitude-frequency characteristics, optimize the elastic and dissipative parameters of suspensions, optimize their number and location, and also monitor the movements of arbitrary points at which various units are located.

The importance of correct specification of tribological parameters in dynamical systems modelling

When modelling the behaviour of dynamical systems, the friction phenomenon cannot be neglected. Dry and fluid friction may occur, but dry friction has more severe effects upon the behaviour of the systems, based on the fact that the introduced discontinuities are more important. In the modelling of dynamical systems, dry friction is the main cause of occurrence of the bifurcation phenomenon. These aspects become more complex if, in the case of dry friction, static and dynamic frictions are put forward. The behaviour of a simple dynamical system is studied, consisting in a prismatic body linked to the ground by a spring, placed on a conveyor belt. The theoretical model is described by a nonlinear differential equation which after numerical integration leads to the conclusion that the steady motion of the prism is an un-damped oscillatory motion. The system was qualitatively modelled using specialised software for dynamical analysis. It was impractical to obtain a steady uniform translational motion of a rigid, therefore the conveyor belt was replaced by a metallic disc in uniform rotation motion. The attempts to compare the CAD model to the theoretical model were unsuccessful because the efforts of selecting the tribological parameters directed to the conclusion that the motion of the prism is a damped oscillation. To decide which of the methods depicts reality, a test-rig was assembled and it indicated a sustained oscillation. The conclusion is that the model employed by the dynamical analysis software cannot describe the actual model and a more complex model is required in the description of the friction phenomenon.

Lorentz invariance of absorption and extinction cross sections of a uniformly moving object

The energy absorption and energy extinction cross sections of an object in uniform translational motion in free space are Lorentz invariant, but the total energy scattering cross section is not. Indeed, the forward-scattering theorem holds true for co-moving observers but not for other inertial observers. If a pulsed plane wave with finite energy density is incident upon an object, the energies scattered, absorbed, and removed from the incident signal by the object are finite. The difference between the energy extinction cross section and the sum of the total energy scattering and energy absorption cross sections for a non-co-moving inertial observer can be either negative or positive, depending on the object's velocity, shape, size, and composition. Calculations for a uniformly translating, solid, homogeneous sphere show that all three cross sections go to zero as the sphere recedes directly from the source of the incident signal at speeds approaching c, whether the material is a plasmonic metal (e.g., silver) or simply a dissipative dielectric material (e.g., silicon carbide).

Electromagnetic pulse scattering by a spacecraft nearing light speed.

Humans will launch spacecraft that travel at an appreciable fraction of the speed of light. Spacecraft traffic will be tracked by radar. Scattering of pulsed electromagnetic fields by an object in uniform translational motion at relativistic speed may be computed using the frame-hopping technique. Pulse scattering depends strongly on the velocity, shape, orientation, and composition of the object. The peak magnitude of the backscattered signal varies by many orders of magnitude, depending on whether the object is advancing toward or receding from the source of the interrogating signal. The peak magnitude of the backscattered signal goes to zero as the object recedes from the observer at a speed very closely approaching light speed, rendering the object invisible to the observer. The energy scattered by an object in motion may increase or decrease relative to the energy scattered by the same object at rest. Both the magnitude and sign of the change depend on the velocity of the object, as well as on its shape, orientation, and composition. In some cases, the change in total scattered energy is greatest when the object is moving transversely to the propagation direction of the interrogating signal, even though the Doppler effect is strongest when the motion is parallel or antiparallel to the propagation direction.

Time-domain electromagnetic scattering by a sphere in uniform translational motion

Scattering by a uniformly translating sphere of a pulse that modulates the amplitude of a linearly polarized plane wave was formulated using the frame-hopping method involving a laboratory inertial reference frame and the sphere's comoving inertial reference frame. The incident signal was defined in the laboratory frame and transformed to the comoving frame with the Lorentz transformation, thereby altering the incident signal's spectrum, direction of propagation of the carrier plane wave, and the direction of the incident electric field, depending on the sphere's velocity. In the comoving frame, the incident signal was Fourier-transformed to the frequency domain, and the scattered field phasors were computed in all directions using the constitutive parameters of the material of the sphere at rest. The scattered signal in the comoving frame was obtained using the inverse Fourier transform. Finally, the scattered signal in the laboratory frame was obtained by inverting the original Lorentz transformation. The backscattered signal was found to depend strongly on the sphere's velocity, when the sphere's speed is an appreciable fraction of the speed of light in free space. The change in the backscattered signal compared with the backscattered signal from a stationary sphere is the greatest when the sphere's velocity is either parallel or antiparallel to the direction of propagation of the incident signal. The backscattered signal is also affected by motion transverse to the incident signal's direction of propagation; then, the backscattered signal depends on whether or not the motion is aligned with the direction of the incident electric field.

Diffraction by a half-plane in uniform translational motion revisited

A problem is reconsidered of time harmonic, electromagnetic diffraction by a perfectly conducting half-plane moving in free space with a constant velocity. Similarities and differences between stationary and moving diffraction have been discussed.

Revealing the Mystery of the Galilean Principle of Relativity. Part I: Basic Assertions

As Galileo has formulated, one cannot detect, once embarked in a uniform translational motion, and not receiving any information from the outside, how fast he is moving. Why? No one that we recall of, has worked out the answer of this question, although the Galilean Principle of Relativity (GPR), constituted a major ingredient of the Special Theory of Relativity (STR). Thus, consider a quantum mechanical object of “clock mass” M0 (which is just a mass), doing a “clock motion”, such as rotation, vibration, etc., with a total energyE0, in a space of size ℛ0. Previously we have established that, if the mass M0 is multiplied by an arbitrary numberγ, then through the relativistic or non-relativistic quantum mechanical description of the object (which ever is appropriate to describe the case in hand), the size ℛ0 of it, shrinks as much, and the total energyE0,concomitantly, increases as much. This quantum mechanical occurrence yields, at once, the invariance of the quantityE0M0ℛ02with regards to themass change in question, the object being overall at rest; this latter quantity is, on the other hand, as induced by the quantum mechanical framework, necessarily strapped to h2, the square of the Planck Constant. But this constant is already, dimension wise, Lorentz invariant. Thus, any quantity bearing the dimension of h2, is Lorentz invariant, too. So is then, the quantity E0M0ℛ02 (no matter how the size of concern lies with respect to the direction of uniform translational motion) that would come into play. Thence, the quantum mechanicalinvarianceof thequantityE0M0ℛ02 with regards to an arbitrary mass change, comes to be identical to the Lorentz invariance of this quantity, were the object brought to a uniform translational motion. It is this prevalence, which displays, amazingly, the underlying mechanism, securing the end results of the STR, and this via quantum mechanics. The Lorentz invariant quantum mechanical architecture, E0M0ℛ02∼h2, more fundamentally, constitutes the answer of the mystery drawn by the GPR. In this article, we frame the basic assertions, which will be used in a subsequent article, to display the quantum mechanical machinery making the GPR, and to draw the bridge between the GPR and the architecture, we disclose.

Electromagnetic radiation from moving, pulsed source distributions: The 3D time-domain relativistic Doppler effect

The pulsed electromagnetic field radiated by distributed electric-current and magnetic-current sources in uniform translational motion is analyzed within the framework of the special theory of relativity. The relevant Lorentz transformations are used to exhibit the general structure of the field as it is experienced by a stationary observer. In particular, the differences in the transmitted and received pulse shapes are discussed, which are manifestations of the 3D time-domain relativistic Doppler effect. Applications are found in Doppler radar and spaceflight telemetry.

Phenomenological model of interaction of a plate with a flow

In the present paper, a finite-dimensional phenomenological model of unsteady interaction of a rigid plate with a flow is proposed. It is assumed that the plate performs translational motion across the flow. The internal dynamics of the flow is modeled by the attached second order dynamical system. It is shown that the model allows satisfactory agreement with experimental data. With the developed model an inverse problem of dynamics is examined for the situation where the plate performing uniform translational motion at some moment begins uniform deceleration and finally stops. It is shown that for sufficiently large values of the plate acceleration for some time range the flow does not resist the motion of the plate but “accelerates” it. It is shown also that the equations of motion in the context of the proposed model can be reduced to the integro-differential form, and comparison with the known model of S. M. Belotserkovsky is performed. The structural resemblance of the motion equations for a body in flow in both models is noted. The domain of applicability of the quasi-stationary model is examined.

Motion Estimation in the 3-D Gabor Domain

Motion estimation methods can be broadly classified as being spatiotemporal or frequency domain in nature. The Gabor representation is an analysis framework providing localized frequency information. When applied to image sequences, the 3-D Gabor representation displays spatiotemporal/spatiotemporal-frequency (st/stf) information, enabling the application of robust frequency domain methods with adjustable spatiotemporal resolution. In this work, the 3-D Gabor representation is applied to motion analysis. We demonstrate that piecewise uniform translational motion can be estimated by using a uniform translation motion model in the st/stf domain. The resulting motion estimation method exhibits both good spatiotemporal resolution and substantial noise resistance compared to existing spatiotemporal methods. To form the basis of this model, we derive the signature of the translational motion in the 3-D Gabor domain. Finally, to obtain higher spatiotemporal resolution for more complex motions, a dense motion field estimation method is developed to find a motion estimate for every pixel in the sequence.

Stability analysis of uniform and non-uniform annular passages conducting incompressible laminar flows for small and large amplitude oscillatory motions of the outer cylinder

A computational method is developed involving the simultaneous integration of the Navier–Stokes and structural equations for the purpose of studying the stability of concentric annular passages conducting incompressible laminar flows. It is assumed that one side of the annulus, i.e. the centre-body, is fixed and the outer cylindrical duct is flexibly supported. The outer cylinder is displaced from its equilibrium position and is then released. In this situation, the fluid part of the problem is solved by an accurate method using a three-point backward implicit scheme, followed by a pseudo-time iteration using an artificial compressibility factor. The fluid equations are discretized in space based on a finite-difference formulation and primitive variables, for which stretched staggered grids are used. The resulting equations are cast in delta form and are solved using an ADI scheme. The fluid forces acting on the vibrating cylinder are calculated from the integration of the unsteady pressure and shear stresses resulting from the unsteady primitive variables calculated. The equations of motion of the structure, subjected to the calculated fluid forces are solved using the Runge–Kutta scheme to obtain the displacement of the moving cylinder. The problem is solved: (a) for small-amplitude motions, by means of the so-called mean position (MP) analysis and (b) for large amplitude oscillations of the outer cylinder for which a time-dependent coordinate transformation (TDCT) is used to fix the computational domain. Both these approaches (MP and TDCT) are applied to uniform and non-uniform (backstep-shaped) annuli for translational motion of the cylinder. The problem is also solved for (i) rocking motion and uniform annuli and (ii) translational motion for diffuser-shaped annuli, with only MP analysis. When the MP analysis is considered, it is shown that, for translational motion of the outer cylinder, the most stable configuration is that of a uniform geometry and the least stable one is the backward step geometry. For rocking motion in uniform annular geometry, for some system parameters and high enough flow velocity, the outer cylinder can develop flutter (limit-cycle oscillation). The comparison between the results of MP and TDCT analyses for uniform and backstep geometries for translational motion of the cylinder indicates that the outer cylinder is less stable when TDCT is used and the coupled frequency of oscillation is also changed considerably.

Electromagnetic wave scattering from moving surfaces with high-amplitude corrugated pattern

This paper deals with the problem of electromagnetic wave scattering from rough surfaces. By means of a generalized Floquet modal representation an analytic solution can be found that is valid for any Fourier-expandable surface pattern, with no limitation on the corrugation amplitude. By means of the special relativistic frame-hopping method, the motionless solution is generalized to the case of uniform translational relative motion between the surface and the observer. Plane-wave simplification techniques are employed to minimize the algebraic complexity of the field covariance transformations. A detailed signal analysis of the electromagnetic scattered field is performed in both the frequency and the time domains.

An analysis of the efficiency of different SNR-scalable strategies for video coders

In this paper, we analyze the efficiency of three signal-to-noise scalable strategies for video coders using single-loop motion-compensated prediction (MCP). In our analysis, we assume the video sequences have uniform and constant translational motion and we model MCP as a stochastic filter. We also assume an exponential model for the distortion-rate function of the intraframe coding. The analysis is divided into two parts: the steady-state analysis and the transient analysis. In the first part, only the steady-state response of the coders is taken into account, and, thus, this analysis allows us to asses approximately the efficiency of coders with long input sequences. The transitory analysis considers both the transient and the steady-state responses of the coders, which makes it appropriate to analyze coders using periodic intraframes or with short input sequences. To validate our analysis, theoretical results have been compared to results from encodings of real video sequences using the scalable adaptive motion compensated wavelet video coder. We show that our theoretical analysis effectively describes qualitatively the main trends of every video coding strategy.

SPEED OF GRAVITY AND GRAVITOMAGNETISM

A vJ/c correction to the Shapiro time delay seems verified by a 2002 Jovian observation by VLBI. In this Essay, this correction is interpreted as an effect of the aberration of light in an optically refractive medium which supplies an analog of Jupiter's gravity field rather than as a measurement of the speed of gravity, as it was first proposed by other authors. The variation of the index of refraction is induced by the Lorentz invariance of the weak gravitational field equations for Jupiter in a uniform translational slow motion with velocity vJ=13.5 km / s . The correction on time delay and deflection is due not to the Kerr (or Lense-Thirring) stationary gravitomagnetic field of Jupiter, but to its Schwarzschild gravitostatic field when measured from the barycenter of the solar system.

An essential approach to the architecture of diatomic molecules: 2. How are size, vibrational period of time, and mass interrelated?

In our previous article, we arrived at an essential relationship for T, the classical vibrational period of a given diatomic molecule, at the total electronic energy E; i.e., $$T = [4\pi ^2 /(\sqrt {n_1 n_2 } h)]\sqrt {g\mathcal{M}_0 m_e } R_0^2 $$ , where ℳ0 is the reduced mass of the nuclei; m e is the mass of the electron; R is the internuclear distance; g is a dimensionless and relativistically invariant coefficient, roughly around unity; and n 1 and n 2 are the principal quantum numbers of electrons making up the bond(s) of the diatomic molecule, which, because of quantum defects, are not integer numbers. The above relationship holds generally. It essentially yields T ∼ R 2, for the classical vibrational period versus the square of the internuclear distance in different electronic states of a given molecule, which happens to be an approximate relationship known since 1925 but not understood until now. For similarly configured electronic states, we determine n 1 n 2 to be R/R 0, where R is the internuclear distance in the given electronic state and R 0 is the internuclear distance in the ground state. Furthermore, from the analysis of H2 spectroscopic data, we found out that the ambiguous states of this molecule are configured like alkali hydrides and Li2. This suggests that, quantum mechanically, on the basis of an equivalent H2 excited state, we can describe well, for example, the ground state of Li2. On the basis of this interesting finding, herein we propose to associate the quantum numbers n 1 and n 2 with the bond electrons of the ground state of any diatomic molecule belonging to a given chemical family in reference to the ground state of a diatomic molecule still belonging to this family but bearing, say, the lowest classical vibrational period, since g, depending only on the electronic configuration, will stay nearly constant throughout. This allows us to draw up a complete systematization of diatomic molecules given that g (appearing to be dependent purely on the electronic structure of the molecule) stays constant for chemically alike molecules and n 1 n 2 can be identified to be R 0/R 00 for diatomic molecules whose bonds are electronically configured in the same way, R 00 then being the internuclear distance of the ground state of the molecule chosen as the reference molecule within the chemical family under consideration. Our approach discloses the simple architecture of diatomic molecules, otherwise hidden behind a much too cumbersome quantum-mechanical description. This architecture, telling how the vibrational period of time, size, and mass are determined, is Lorentz-invariant and can be considered as the mechanism of the behavior of the quantities in question in interrelation with each other when the molecule is brought into uniform translational motion or transplanted into a gravitational field or, in fact, any field with which it can interact.

Electromagnetic Wave Scattering By a Perfectly Conducting Wedge in Uniform Translational Motion

The exact relativistic solution to the problem of electromagnetic wave scattering by a perfectly conducting wedge in uniform translational motion is obtained on the ground of the Frame Hopping Method; a field representation in terms of plane-wave spectra allows us to apply Special Relativity covariance relations in terms of simple alteration rules for the wave parameters of the spectral components. Numerical simulations based on the analytic evaluation of Doppler frequency spectra, as measured by a fixed observer, are presented.

Electric fields associated with moving phase boundaries during martensitic transformation

Phase transformations in metals are considered in terms of non-equilibrium continuum thermodynamics. The evolution of a heterophase system in thermal and electric fields is described by a self-consistent set of differential equations. Special attention is paid to the thermoelectric properties of phase boundaries. A one-dimensional model for uniform translational motion of a plane interface is developed, the spatial distributions of temperature and electric charge, current and potential are calculated.

Neural fuzzy motion estimation and compensation

Neural fuzzy systems can improve motion estimation and compensation for video compression. Motion estimation and compensation are key parts of video compression. They help remove temporal redundancies in images. But most motion estimation algorithms neglect the strong temporal correlations of the motion field. The search windows stay the same through the image sequences and the estimation needs heavy computation. A neural vector quantizer system can use the temporal correlation of the motion field to estimate the motion vectors. First- and second-order statistics of the motion vectors give ellipsoidal search windows. This algorithm reduced the search area and entropy and gave clustered motion fields. Motion-compensated video coding further assumes that each block of pixels moves with uniform translational motion. This often does not hold and can produce block artifacts. We use a neural fuzzy system to compensate for the overlapped block motion. This fuzzy system uses the motion vectors of neighboring blocks to map the prior frame's pixel values to the current pixel value. The neural fuzzy system used 196 rules that came from the prior decoded frame. The fuzzy system learns and updates its rules as it decodes the image. The fuzzy system also improved the compensation accuracy. The paper derives both the fuzzy system and the neural learning laws that tune its parameters.

On the Arbitrary Choice Regarding Which Inertial Reference Frame Is “Stationary” and Which Is “Moving” in the Special Theory of Relativity

Einstein's argument on the relativity of simultaneity itself is the first result of the special theory of relativity. This argument is reflected in the structure and functioning of the physical world. The arbitrary nature of the decision regarding the particular inertial reference frame from which the argument on the relativity of simultaneity begins is discussed. It is this arbitrary, or freely made, decision that is the basis for the significance of the argument of the relativity of simultaneity itself on the structure and functioning of the physical world. The same concrete circumstances in the physical world can support either direction in the argument on the relativity of simultaneity, as well as other results, in the special theory (i.e., with either of two inertial reference frames in uniform translational motion relative to one another considered stationary while the other inertial reference frame is considered moving). There are different sets of results in the physical world associated with the choice in direction that is made, for example as concerns the temporal durations of occurrences or the spatial lengths of existents in these inertial reference frames. Experiments testing the equations derived in the special theory that relate the temporal durations of occurrences or the spatial lengths of physical existents in inertial reference frames in uniform motion relative to one another generally have not tested predictions with both of the two inertial reference frames considered, in separate scenarios, the stationary reference frame. It is proposed that empirical tests in two directions be developed and conducted. If empirical results from such tests support the predictions of the special theory, these empirical results would support the thesis that there is a cognitive factor in Einstein's argument on the relativity of simultaneity that affects results derived in the special theory concerning the physical world. One such test is proposed.