Non-inertial Frame Research Articles

Developing an Interactive Simulation for Noninertial Reference Frames

The forces involved in the motion of objects within noninertial reference frames are challenging concepts for introductory and advanced mechanics students. Furthermore, students often struggle to predict the trajectories of an object due to these fictitious forces. While most students encounter noninertial reference frames daily, students often spend most of their physics coursework analyzing situations in which the Coriolis and centrifugal forces are negligible. We developed an interactive and freely accessible simulation of a rotating turntable apparatus that aims to improve understanding of the motion of objects in noninertial reference frames.

Inertial and non-inertial frames of reference: A kinematic approach through video analysis

Nas abordagens introdutórias de Mecânica, seja no ensino superior ou na educação básica, as discussões em torno das diferenças entre os conceitos de referencial inercial e não inercial costumam ser restritas à Dinâmica, especialmente com a definição das leis de Newton, sem análises experimentais. No entanto, a noção de referencial é fundamental para a caracterização dos movimentos, mesmo que do ponto de vista estrito da Cinemática. Neste contexto, objetivamos fundamentar os conceitos de referencial inercial e não inercial a partir da exploração de uma atividade experimental com fins didáticos desenvolvida por meio de videoanálise. Especificamente, investigamos o lançamento de uma pequena bola em três situações de movimento relativo entre dois referenciais: movimento retilíneo uniforme; movimento retilíneo uniformemente variado, com aceleração e velocidade de mesmo sentido; e movimento retilíneo uniformemente variado, com aceleração e velocidade em sentidos opostos. Obtemos uma descrição cinemática embasada no Princípio de Relatividade de Galileu e nas relações de transformação entre referenciais inerciais e não inerciais, além dos ajustes das curvas de movimento obtidas pela videoanálise. Sugerimos que outros aspectos, como: invariância de escala, simultaneidade no tempo, e questões históricas relacionadas aos conceitos de referencial, movimento absoluto e relativo, possam ser encaminhadas nas discussões dos experimentos propostos.

Connection between gravitational and inertial masses of compound objects and the weak equivalence principle

The connection between gravitational and inertial masses of compound objects (e.g. nucleons, nuclei, atoms, and molecules) in the presence of rapid internal motions of their constituent parts is considered. The equality of gravitational and inertial masses of such objects confirming the weak equivalence principle is proven provided that their moving constituent parts are confined. The result is very nontrivial because of a substantial difference between particle dynamics in noninertial frames and gravitational fields. Paradoxically, gravitational effects are different for the same particles moving in the closed box and in the free space. The gravitational and inertial masses are equal to the corresponding kinematic masses. In contrast, gravitational masses of ensembles of noninteracting moving particles cannot be introduced because the total gravitational forces acting on these ensembles do not correspond to their kinematic masses.

Reflected entropy and Markov gap in noninertial frames

Reflected entropy and Markov gap in noninertial frames

CoNi-MPC: Cooperative Non-inertial Frame Based Model Predictive Control

CoNi-MPC: Cooperative Non-inertial Frame Based Model Predictive Control

Hands-on visualization of the effect of fictitious forces with a laser pointer

Inertial motion looks like accelerated motion when observed from the point of view of a non-inertial reference frame. A non-inertial observer can then describe the trajectories by introducing fictitious forces, like the centrifugal and Coriolis forces, that arise from the coordinate change between reference frames. This well-known fact is part of the typical Physics syllabus for undergraduate scientists and engineers, and a number of interesting classroom demonstrations have been discussed in the literature. We present a complementary possibility for the visualization of the effect of fictitious forces by shining a blue laser beam on a rotating platform covered with a phosphorescent vinyl sheet. The laser can be moved in order to simulate inertial motion in the laboratory frame for the trajectory of the laser spot. This gets immediately imprinted in the rotating phosphorescent material resulting in non-inertial trajectories that can be readily observed and compared to the dynamics governed by fictitious forces. Since friction is not considered, this hands-on activity can be considered as a direct demonstration of the effect of pure fictitious forces in and out of the classroom. The approach is simple, inexpensive, fast and non-destructive, and can therefore be very convenient for active lecture demonstrations or individual activities of students. We also describe some educational possibilities of how to use the procedure in the classroom or in the laboratory.

Effects of rotation on the rolling noise radiated by wheelsets in high-speed railways

Railway rolling noise is produced by the vibration of both the wheelsets and the track; the wheelsets dominate the high frequency noise and become increasingly important at high speed. The effect of rotation on the wheelset vibration and noise radiation is investigated using different wheelset models in a rolling noise prediction model for a wide range of speeds. Each wheelset model takes account of the rotation to a different extent. An axisymmetric finite element model of a flexible rotating wheelset is implemented based on a complex exponential formulation and expressed in either an inertial or a non-inertial frame of reference. The model can include the inertial Coriolis and centrifugal forces and is also extended to include stress stiffening. Modes of the rotating wheel with non-zero number of nodal diameters are split into co- and counter-rotating waves with separated natural frequencies. The extent of the frequency separation depends on the shape of the mode and its dominant component of vibration. At common train speeds the frequency shifts due to stress-stiffening and spin-softening effects are found to be small compared with the gyroscopic effects due to the Coriolis forces. The effect of including the inertial Coriolis and centrifugal forces on the overall A-weighted sound power level is less than 0.3 dB below 400 km/h, while for higher train speeds, differences may exceed 1 dB in some one-third octave bands. Overall, these differences are small compared with other sources of uncertainty in rolling noise modelling, confirming that representing the wheel rotation with a moving load approach provides a suitable approximation for use in rolling noise predictions.

An observer's perspective of the Unruh and Hawking effects—Using coherent signals to extract information from a black hole

The Unruh effect is one of the first calculations that explain what one would see when transiting between an inertial reference frame in its quantum field vacuum state and a non-inertial (specifically, uniformly accelerating) reference frame. The inertial reference frame's vacuum state would not correspond to the vacuum state of the non-inertial frame. The observer in the non-inertial frame would see radiation, with a corresponding Bose distribution and a temperature proportional to the acceleration. In this paper, I compute the response of this non-inertial observer to a single frequency mode in the inertial frame and deduce that, indeed, the cumulative distribution (over the observer's proper time) of frequencies observed by the accelerating observer would be the Bose distribution with a temperature proportional to the acceleration. The conclusion is that the Unruh effect (and the related Hawking effect) is generic, in that it would appear with any incoming incoherent state and the Bose distribution is obtained as a consequence of the non-inertial frame's motion, rather than some special property of the quantum vacuum. As a consequence of the analysis of a coherent set of signals, I show how to extract information from the spectrum that an accelerated observer would see (as well as from the radiation from a black hole).

On the Issue of the Trajectory of a Freely Falling Body in Noninertial Frames of Reference

On the Issue of the Trajectory of a Freely Falling Body in Noninertial Frames of Reference

First Principles Description of Plasma Expansion Using the Expanding Box Model

Multi-scale modeling of expanding plasmas is crucial for understanding the dynamics and evolution of various astrophysical plasma systems such as the solar and stellar winds. In this context, the Expanding Box Model (EBM) provides a valuable framework to mimic plasma expansion in a non-inertial reference frame, co-moving with the expansion but in a box with a fixed volume, which is especially useful for numerical simulations. Here, fundamentally based on the Vlasov equation for magnetized plasmas and the EBM formalism for coordinates transformations, for the first time, we develop a first principles description of radially expanding plasmas in the EB frame. From this approach, we aim to fill the gap between simulations and theory at microscopic scales to model plasma expansion at the kinetic level. Our results show that expansion introduces non-trivial changes in the Vlasov equation (in the EB frame), especially affecting its conservative form through non-inertial forces purely related to the expansion. In order to test the consistency of the equations, we also provide integral moments of the modified Vlasov equation, obtaining the related expanding moments (i.e., continuity, momentum, and energy equations). Comparing our results with the literature, we obtain the same fluids equations (ideal-MHD), but starting from a first principles approach. We also obtained the tensorial form of the energy/pressure equation in the EB frame. These results show the consistency between the kinetic and MHD descriptions. Thus, the expanding Vlasov kinetic theory provides a novel framework to explore plasma physics at both micro and macroscopic scales in complex astrophysical scenarios.

Synthetic design and analysis of the new feed cabin mechanism in Five-hundred-meter Aperture Spherical radio Telescope (FAST)

Due to the large weight of the feed cabin, the observation range of the Five-hundred-meter Aperture Spherical radio Telescope (FAST) is limited and unable to cover the galactic center. To solve this problem, a new feed cabin mechanism (NFCM) is designed to replace the heavy rigid components using the novel lightweight cable-driven structure, where the observation-related characteristics are investigated. After dimensional optimization, the observation range is analyzed using a two-level optimization that has explicit graphic-based solutions, the parameter sensitivity is studied by proposing the direct numerical method, and the anti-disturbance ability is discussed using the novel disturbance unit increment method. Numerical simulations indicate that the optimal designed NFCM can achieve required larger observation range with exceptional observation performance. Additionally, considering the two-level control mode of FAST, a novel controller is proposed for the NFCM by addressing dynamics in the non-inertial frame, and the control performance in time and frequency domain is validated using actual observation data, where the NFCM can effectively suppress residual errors from the outer six-cable-driven system in FAST and has satisfactory control robustness in resisting system disturbances.

Dynamic modeling and analysis of a large-scale hoop-column antenna using the referenced nodal coordinate formulation

Hoop-column antenna (HCA) is a popular type of deployable antenna in aerospace engineering. Extracting a precise model and performing a comprehensive dynamic analysis is the foundation for ensuring the HCA works properly in complex space environments. However, the multiscale characteristics and strong nonlinearities make most modeling methods invalid because of low accuracy and efficiency. Dynamic modeling and analysis are conducted for HCA constructed by beams and cables using the referenced nodal coordinate formulation in this work. The straight and initially curved beam elements and pre-tensioned cable elements are introduced based on the absolute nodal coordinate formulation. The HCA is described in a non-inertial frame to separate the overall motion and deformations. The nonlinear dynamic equations of the HCA are firstly linearized around its tensioned equilibrium configuration and natural frequencies and mode shapes are analyzed. The symmetric and antisymmetric mode shapes are observed and corresponding characteristics are revealed. The mistuning ratio is introduced to study the mistuning properties. The nonlinear dynamic responses of the HCA for orbital transfer under finite thrust are simulated. The present work provides a general dynamic modeling approach for linear and nonlinear dynamic analysis of the HCA. The numerical results also provide some guidance for the parameter design and vibration control of the HCA.

Accuracy of BEMT and CFD on the power and trust prediction of tidal turbines

We compute the loads on a model-scale tidal turbine with Blade Element Momentum (BEM) theory and Computational Fluid Dynamics (CFD) simulations, and we compare the results with towing tank tests. CFD simulations are wall-resolved, steady, Reynolds-averaged Navier-Stokes simulations with a k − ω SST turbulence model, where only a 120◦ wedge domain with a single blade is resolved in a non-inertial frame of reference. We undertake a detailed uncertainty analysis to identify the sources of error. BEM uncertainty is computed with a Monte-Carlo approach based on the differences in the predictions of CFD and Xfoil for the sectional lift and drag coefficients,while CFD uncertainty is based on the errors due to the finite number of iterations and spatial resolution. The maximum error of CFD (8.0%) with respect to the experimental data is about half of that of BEM (15.5%) for the power (CP) and the thrust (CT) coefficients and both errors are within 4.1% for CFD and within 7.2% for BEM around the optimal tip-speed ratio (λ = 6.03). The BEM error is within the uncertainty associated with the imprecise knowledge of the sectional lift and drag coefficients. The sectional forces from CFD and BEM disagree at both the tip and the root, resulting in a substantial BEM underprediction of CP at high λ values (up to 15.5%), yet CT is well predicted (within 2.3%) at every λ. The CFD uncertainty is markedly smaller than the error, which is thus mostly due to a modelling error such as the turbulence model, the neglected effect of the support structure, the free surface, and the imprecise knowledge of the input conditions. Overall these results suggest that CFD provides both a maximum error and uncertainty that are substantially smaller than that of BEM, but both methods suffer from modelling errors that require further investigation.

System–environment dynamics of GHZ-like states in noninertial frames

System–environment dynamics of GHZ-like states in noninertial frames

Rotational Dynamics of a Protein under Shear Flow Studied by the Eckart Frame Formalism.

Proteins are natural polymers that play an essential role in both living organisms and biotechnological applications. During certain bioprocessing steps, they can be exposed to significant mechanical stress induced by, for example, shear flow or sonication, resulting in reduced therapeutic efficacy, aggregation, or even a loss of activity. For this reason, there is a need to understand and determine the susceptibility of the protein activity to the experienced mechanical stress. To acquire this knowledge, it is necessary to study the rotational dynamics of the protein. Commonly, the rotational dynamics of soft molecules is interpreted based on a theoretical analysis performed in an inertial laboratory frame. However, the obtained angular velocity mixes pure rotations and vibrations with angular momentum, consequently lacking a clear dynamical interpretation. On the other hand, the use of the noninertial internal Eckart frame allows the determination of pure angular velocity as it minimizes the coupling between the rotational and vibrational degrees of freedom. In the present work, by conducting open-boundary molecular dynamics simulations and exploiting the Eckart frame formalism, we study the rotational dynamics of a small protein under the shear flow of various strengths. Our results show that the angular velocity increases nonlinearly with increasing shear rate. Furthermore, the protein gains vibrational angular momentum at higher shear rates, which is reflected in the higher angular velocity computed by employing the Eckart frame formalism and confirmed by analysis of the contributions to the total kinetic energy of the biomolecule.

Heat source/sink effect in radiative flow of hybrid nanofluid subject to noninertial frame

Hybrid nanofluids have achieved a lot of interest because they have the ability to improve the thermophysical characteristics for the applicable applications. In the context of heat transport, thermal conductivity performance is more important than other physical characteristics. Therefore, a theoretical analysis is presented for heat transport and nanoparticle concentration on the thermal conductivity of hybrid nanofluid Cu-Al2O3/kerosene oil. Thus, the mathematical model is based on the thermophysical properties of hybrid nanofluids. The heat transport analysis is analyzed with the help of multiple solutions. The stretching/shrinking parameter and mass flux constraint controlled the motion of the flow. A collocation method is used with bvp4c to produce numerical results. In comparison to mono nanofluids, it is noted that the energy transport is significantly improved by the inclusion of a hybrid nanoparticle mixture. Moreover, the shrinking parameter and magnetic field parameter as well as particle volume fraction significantly exhibit the dual nature of the solutions. Further, due to increased suction strength the velocity in x- and y-directions show opposite behavior.

N-partite Entanglement Measures of GHZ States in a Non-inertial Frame

N-partite Entanglement Measures of GHZ States in a Non-inertial Frame

Radar Method in a Uniformly Accelerated Reference Frame

The purpose of this work is to generalize the radar method known for the inertial frame of reference to the case of a uniformly accelerated frame of reference.The derivation of the corresponding formulas is based on the standard for the theory of relativity metric of a uniformly accelerated Möller frame of reference without applying any space-time transformation between some auxiliary inertial frame and the accelerated frame. To solve the problem of determining the trajectory of a light beam, depending on the initial direction of propagation, Fermat’s principle is used. To calculate the flight time of a photon to an object, knowing its coordinates, the condition of the light-likeness of the interval for the propagation of light is additionally introduced.The resulting trajectory of the light particle is an arc of a circle. For a small area near the source, the photon trajectory coincides with the parabolic trajectory of a classical corpuscle. An equation has been derived for the direction in which the radio signal is sent. The actual location of the object is not in the direction of the initial motion of the photon, but somewhat lower. The value of the angle of gravitational refraction for a closely spaced resting object is calculated. The further the object is in the “horizontal” direction, the greater the angle of refraction. The flight time of the light signal to the object is found. The signal emitted in the direction that forms an acute angle with the direction of acceleration leads the radio signal in the inertial frame of reference. Therefore, for a close object located above the radiation source, the calculated Shapiro delay time is negative. The coordinates of the remote object are also calculated.The totality of the obtained equalities completely determines the radar method. The resulting equalities, perhaps, allow for experimental verification.

Influences of noisy channels on quantum coherence and entanglement of W state in noninertial frame

Via using l 1-norm of quantum coherence and π–tangle, we investigate influences of amplitude-damping and depolarizing channels on quantum coherence and entanglement for W state of Dirac fields when two observers are in accelerating motion. We find that quantum entanglement vanishes for all values of acceleration if at least one qubit is under noisy channels. But quantum coherence does not vanish even at infinite acceleration if only one subsystem is under noisy channels. We also find that, unlike the depolarizing environment, the amplitude-damping environment can destroy symmetric properties of quantum entanglement with respect to two accelerated observers. These results will further enrich our understanding on the relation between quantum coherence and entanglement.

Observing single particles beyond the Rindler horizon

We show that Minkowski single-particle states localized beyond the horizon modify the Unruh thermal distribution in an accelerated frame. This means that, contrary to classical predictions, accelerated observers can reveal particles emitted beyond the horizon. The method we adopt is based on deriving the explicit Wigner characteristic function for the complete description of the quantum field in the noninertial frame and can be generalized to general states.Received 1 December 2021Revised 9 March 2022Accepted 21 March 2023DOI:https://doi.org/10.1103/PhysRevA.107.L030203©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasUnruh effectAtomic, Molecular & Optical