Noninertial Reference System Research Articles

Effect of an accelerating metro cabin on the diffusion of cough droplets

Coronaviruses being capable of spreading through droplet contamination have raised significant concerns regarding high-capacity public rail transport, such as the metro. Within a rapidly moving railcar cabin, the internal airflow lags behind the bulkhead, generating internally induced airflow that accelerates droplet dispersion within a non-inertial reference system. This study investigates the impact of acceleration on the diffusion of cough droplets of varying sizes using computational fluid dynamics. The modified k–ε equation in ANSYS® Fluent was utilized to simulate droplet diffusion under different body orientations by adjusting the inertial force correction source term. Results indicate that droplets in the middle size range (50–175 μm) are primarily influenced by inertial forces, whereas smaller droplets (3.5–20 μm) are predominantly controlled by air drag forces. Regardless of facial orientation, the outlet of high-capacity public rail transport poses the highest risk of infection.

АЛГОРИТМИЗАЦИЯ ОПРЕДЕЛЕНИЯ СООТВЕТСТВИЙ МЕЖДУ ДИНАМИЧЕСКИМИ ПАРАМЕТРАМИ РЕАКТИВНЫХ ДВИЖЕНИЙ КОНСТРУКТИВНЫХ ЭЛЕМЕНТОВ ЗДАНИЙ ОТ ДИНАМИЧЕСКИХ ВОЗДЕЙСТВИЙ

In this paper, two algorithms have been developed that allow us to obtain in more detail, depending on the kinematic characteristics of structural elements and initial conditions, the estimated dynamic characteristics of external influences as the results of the reactive behavior of structural elements of buildings and structures to these influences. Variants of reactive motions in inertial and non-inertial reference systems from static and dynamic wind pressure are considered. Two problems related to finding correspondences between the resultant acting forces (F) and changes in the velocities and accelerations of reactive movements of structural elements over a certain time interval have been solved.

Vehicle-bridge coupling vibration of curved beam bridge under earthquake excitation

Based on the non-inertial reference system, the vehicle model of four freedom degrees is used to establish the vehicle-bridge coupling dynamic system model of the curved beam in space. Considering the vehicle-bridge coupling vibration characteristics under the non-uniform seismic excitation at the two supports of the bridge, the three-dimension space curvilinear-vehicle coupling dynamic control equation is established based on the Hamiltonian principle. Then the coupling dynamic control equation of the vehicle and bridge is numerically analyzed by the method of separating variables.

Nonlinear Dynamic Characteristics of Marine Rotor‐Bearing System under Heaving Motion

In this paper, the influence of the heaving motion on the nonlinear dynamic behavior of the rotor‐bearing system is considered. First, a mathematic model of the marine rotor‐bearing system is developed on the short bearing theory in the noninertial reference system, in which the heaving motion is taken into account. Then its dynamic characteristics are analyzed based on the numerical integration method, such as the bifurcation diagram, the largest Lyapunov exponents (LLE), the steady‐state response, and the rotor orbit and its Poincaré map. The results indicate that heaving motion has a great effect on the dynamics of the rotor system, which exhibits a period 1 motion at low rotating speed, with the increase of the rotating speed, the phenomena of the quasiperiodic, period 2, and double Hopf bifurcations appear. Its dynamic performance presents a period 1 motion, period 2, quasiperiodic, and chaotic oscillation.

Generation of droplets via oscillations of a tapered capillary tube filled with low-viscosity liquids

Droplet formation via the oscillations of a tapered capillary tube is experimentally and numerically investigated using incompressible, low-viscosity Newtonian liquids. As in many other common methods of droplet generation, this technique features a transient flow that is directed out of a nozzle. However, due to the interactions of the oscillations, the tube, and the fluids, the flow rate upstream of the nozzle cannot be directly obtained. In this study, the motion of the tube is measured under the activation of a specific waveform, and the flow inside the tube and drop formation are further numerically studied using a non-inertial reference system in which the tube is stationary. The mechanism of ejection is quantitatively explained by analyzing the temporal variation in the velocity and pressure distributions inside the tube. The dynamics of drop formation, the drop velocity, and the drop radius are studied as functions of the dimensionless groups that govern the problem, including the Ohnesorge number Oh, the Weber number We, the gravitational Bond number G, and various length scale ratios. The results show that droplets are generated due to the inertia of the liquid and velocity amplification in the tapered section. By influencing the balance between the viscous effect and inertial effect of the liquid along the entire tube, the length scale ratios affect the evolution of the transient flow at the nozzle and eventually influence the drop radius and velocity. For liquids with viscosities close to that of pure water, the critical Reynolds number, at which a drop can be generated, linearly depends on the Z number (the reciprocal of Oh) at the nozzle.

Effect of angular aberration using the example of the laser location of a spacecraft in a geosynchronous orbit

A mathematical model for the laser location of a spacecraft in a geosynchronized orbit is generated in a rotating reference system. A formula for calculating the angular aberration that appears when the noninertial reference system is considered is derived. The maximum and minimum values of angular aberration are calculated for when the laser station is at the Equator.

Two-dimensional viscous numerical simulation of liquid sloshing in rectangular tank with/without baffles and comparison with potential flow solutions

A viscous fluid model based on non-inertial reference system is developed for the problem of liquid sloshing in rectangular tank with/without baffles. The accuracy of the numerical model is validated against available theoretical solutions, experimental data and numerical predictions by linear and nonlinear potential flow models and different Navier–Stokes solvers. The numerical examinations indicate that the dissipative effects have significant influence on the sloshing responses in both non-baffled and baffled tanks. The sloshing responses that are associated with the natural frequencies can be finally damped out due to the physical dissipations, while they are entirely retained in the potential solutions, which accounts for the general over-predictions of sloshing amplitudes by the potential flow theory. The sloshing in baffled tank involves more dissipation due to the stronger vortical flow. The resonant frequency and amplitude are highly dependent on the baffle width and position. The relative sloshing amplitudes around the resonant condition are found to decrease with the excitation amplitude in a power law. The necessity of using viscous fluid model for sloshing predictions is addressed. The extremely long numerical computations have to be carried out in order to obtain convincing stable solutions, especially for the weakly damped sloshing motion.

Spin-torsion coupling and gravitational moments of Dirac fermions: Theory and experimental bounds

We discuss the quantum dynamics of the Dirac fermion particle in a gauge gravitational field. The minimal as well as the Pauli-type nonminimal coupling of a fermion with external fields is studied, bringing into consideration the notions of the translational and the Lorentz gravitational moments. The anomalous gravitomagnetic and gravitoelectric moments are ruled out on the basis of the covariance arguments. We derive the general Foldy-Wouthuysen transformation for an arbitrary configuration of the gauge gravitational field without assuming it weak. Making use of the Foldy-Wouthuysen Hamiltonian for the Dirac particle coupled to magnetic field in a noninertial reference system, we analyze the recent experimental data and obtain bounds on the spacetime torsion.

Introduction to the Theory of Relativity of Non-Inertial Systems and Mechanics of the Universe

The physical nature of inertia is explored. Authors, based on Mach’s principle, offer hypothesis of the induction nature of inertia and theory, which allows extend the principle of relativity to the non-inertial reference systems. The system of differential equations, which eliminates the shortcomings of Newtonian mechanics and Special Theory of Relativity (STR) was composed according to this theory. Row of concrete calculations and explanations are made using the theory. Reason of constancy orbital velocities of galaxies is found out and way of its calculations is shown. Existence of dark matter and the new particles (neutralinos, axons, space vacuum etc.) is prejudiced. Axial deviation of the ray of light in gravitational field is explained and calculated. An example of calculation of the Mercury’s orbital motion is made and complex planets’ trajectories are explained by the action of new field with induction nature. Flat rotation of celestial bodies and shaping of planets’ rings (like the Saturn’s rings) are explained. Indistinguishability of Doppler and Einstein’s effects for terrestrial observer is shown.

APPLICATION OF AN EULER SOLVER TO SELECTED PROBLEMS IN FLIGHT DYNAMICS

Several applications of a Euler solver with the formulation of the flow equations in the noninertial reference system with steady and unsteady flow analysis are presented. The steady‐flow applications include determination of aerodynamic derivatives with respect to angular velocity and analysis of vortical flow over a delta wing at high angles of attack with the determination of aerodynamic coefficients and analysis of vortex breakdown. The unsteady flow analysis is applied in the simulation of a rapid manoeuvre for the determination of unsteady forces. The results of this simulation are compared with results of simulations using steady‐flow approximation in order to assess the advantages of unsteady flow analysis in the simulation of aircraft manoeuvres.

Why does the motorbike feather?

The problem of motorbike feathering has been analysed by writing the angular momentum theorem for non-inertial reference systems. The acceleration, for which the ideal line joining the median points of the axles of the two wheels makes an angle θ with the horizontal, has been calculated neglecting air friction and considering that the motorbike starts feathering at low speeds. From this analysis it is also possible to determine the characteristic angle θ0 for which no acceleration is necessary to maintain the feathering of the motorbike.

The importance of non-inertial reference systems in some problems of translational dynamics

The importance of using non-inertial reference systems in some problems of translational dynamics is addressed. For this, a problem is presented with its detailed solution. Typical misconceptions and preconceptions of students in this subject are discussed.

Routh's equations for general nonholonomic mechanical systems of variable mass

In this paper, Routh's equations for the mechanical systems of the variable mass with nonlinear nonholonomic constraints of arbitrary orders in a noninertial reference system have been deduced not from any variational principles, but from the dynamical equations of Newtonian mechanics. And then again the other forms of equations for nonholonomic systems of variable mass are obtained from Routh's equations.

Note on the Cohen, Moses and Rosenblum letter about the slow-clock transport synchronization in noninertial reference systems

CO~EN, MOSES and I~OSENBLUI~ (t) deal with the measured time differences in using the slow-clock transport synchronization (SCTS), and light signal sinehronization (LSS) in noninertial reference systems. The SCTS and the LSS are experimentally equivalent operations only in inertial reference systems. The SCTS contains implicitly an additional conventional restrictions, equivalent with the choice of the Einstein specialrelativistic synchronization (2). In noninertial reference systems the use of the Einstein synchronization is impossible. Therefore, when synchronizing with the SCTS in noninert ial reference systems, an additional (~ hidden error ~> is introduced in the procedure. Whe using the SCTS in noninert ial reference systems, we have to do with the superposition el two e]fects:

Mathematical model of constraint problem of three bodies in noninertial reference system

Many problems in the study of the motion of artificial earth satellites involve the introduction of a nonrotating geocentric system of coordinates [i, 3]. Such a system is not an inertial one, principally because of the earth's rotation about the barycenter (center of gravity) of the earth-moon system 9 This gives rise to inertial force perturbations, quite largely affecting high-altitude and particularly geostationary satellites [2]. In accordance with the principle of relativity pertaining to compensation of noninertial reference systems, it is necessary to add d'Alambert inertia forces to the active forces of gravitation. On the basis of the formulation [3, 7] of the boundary-value problem of three bodies, those forces can be determined through reversing the problem of two bodies and correctly accounting for the variability of the elliptical parameters of the orbit in which the perturbing body moves. The boundary-value problem of three bodies, its approximate solutions and integrals were used in earlier studies [4, 6] for calculating the trajectories of artificial cosmic bodies.

Light propagation in noninertial reference systems

The fundamental equations of geometric optics are obtained in noninertial reference systems associated with arbitrarily moving observers. The electromagnetic wave being propagated in an arbitrary space-time metric background is characterized by the observed quantitiesκ0 (relative frequency), n (the unit vector indicating the direction of wave propagation), and f⊥ (the complex spatial polarization vector). Equations are obtained which govern the observed change inκ0, n, f⊥ for transfer along the rays (isotropic geodesies) as a function of the accelerations, rotations, and deformations in the reference system. It is shown that the kind of polarization does not change during transfer along the ray and is independent of the selection of the reference system. The angular velocity of the polarization vector is determined.

Finsler method for studying noninertial reference systems of a charge

Finsler method for studying noninertial reference systems of a charge

Non-lorentz transformations of reference systems

The structure of transformations is investigated which describe the transition from an inertial reference system to a noninertial one and conversely. As a result of such transition the curvature of the space of events is modified, and one is thus able to discuss its observational character. This leads to a new interpretation of the general relativity theory in which the space curvature is now related only to the noninertial motion of the observer. Transition from a noninertial reference system corresponding to the Schwarzschild space to an inertial reference system (plane space) is considered as an example.