Non-inertial Frame Research Articles

MOND as a Transformation Between Non-inertial Reference Frames Via Sciama’s Interpretation of Mach’s Principle

MOND as a Transformation Between Non-inertial Reference Frames Via Sciama’s Interpretation of Mach’s Principle

System modeling and fuzzy adaptive PI sliding-mode control of a novel ship-mounted cable-based bulkhead cleaning robot

Ship cleaning poses significant risks and consumes considerable time, primarily due to the irregular hull surface geometry and the unpredictable ship motion induced by wave excitation. To address this challenge and achieve efficient, autonomous cleaning, a spatial variable structure cable-based bulkhead cleaning robot (SC-R) is proposed. Unlike traditional cable-driven parallel mechanisms (CDPMs), SC-R operates in a non-inertial frame, whereby its motion is subject to continuous and unpredictable ship motion. Consequently, SC-R exhibits intricate dynamic characteristics, posing a significant hurdle for controller design. To solve this problem, a sliding-mode controller is proposed for SC-R. Specifically, the dynamic model of SC-R, which includes ship motion and various disturbing forces, is systematically established using the Newton-Euler method. Furthermore, a fuzzy adaptive PI sliding-mode controller (FAPI-SMC) is specifically proposed to enhance the convergence speed and robustness of SC-R. The stability of the closed-loop system is analyzed using Lyapunov theory, and the tracking error is proved to be eventually bounded. Finally, the availability of this theory is confirmed by simulation and experiment. It is shown that FAPI-SMC can achieve a satisfactory control effect in practice.

The water bottle flipping experiment: a quantitative comparison between experiments and numerical simulations

Abstract The water bottle flip experiment is a recreational, non-conventional illustration of the conservation of angular momentum. When a bottle partially filled with water is thrown in a rotational motion, water redistributes throughout the bottle, resulting in an increase of moment of inertia and thus a decrease in angular velocity, which increases the probability of it falling upright on a table as compared with a bottle filled with ice. The investigation of this phenomenom is accessible to undergraduate students and should allow them to gain better understanding of combined translational and rotational motions in classical mechanics. We report a series of detailed experiments that are quantitatively compared with numerical calculations based on a simple theoretical framework in which the water volume is decomposed into thin slices of a rigid body that are subjected to fictitious forces in the non-inertial frame of the spinning bottle. This model also allows us to capture and predict other experimental configurations. Finally, we discuss additional counter-intuitive effects that contribute to bottle stabilization on landing.

Online Handwriting Recognition Method with a Non-Inertial Reference Frame Based on the Measurement of Linear Accelerations and Differential Geometry: An Alternative to Quaternions.

This work describes a mathematical model for handwriting devices without a specific reference surface (SRS). The research was carried out on two hypotheses: the first considers possible circular segments that could be made during execution for the reconstruction of the trace, and the second is the combination of lines and circles. The proposed system has no flat reference surface, since the sensor is inside the pencil that describes the trace, not on the surface as in tablets or cell phones. An inertial sensor was used for the measurements, in this case, a commercial Micro-Electro Mechanical sensor of linear acceleration. The tracking device is an IMU sensor and a processing card that allows inertial measurements of the pen during on-the-fly tracing. It is essential to highlight that the system has a non-inertial reference frame. Comparing the two proposed models shows that it is possible to construct shapes from curved lines and that the patterns obtained are similar to what is recognized; this method provides an alternative to quaternion calculus for poorly specified orientation problems.

An alternative to the Euler equation of rigid body rotational dynamics

The Euler equation provides a convenient framework for studying the rotational dynamics of rigid bodies in solid mechanics. While this equation is written from the point of view of an inertial observer, it is implemented in a non-inertial ancillary coordinate system attached to the rigid body and the equations of the rotation are consequently expressed in this ancillary system. We examine how the rotational dynamics of rigid bodies can be described by the inertial observer directly in the inertial coordinate system (instead of employing an ancillary non-inertial frame), and derive the differential equations of the rotation in this inertial system. This approach can have advantages in situations where the rigid body has both translational motion in addition to rotational motion.

Investigation of a Modified Wells Turbine for Wave Energy Extraction

The Oscillating Water Column (OWC) is the most promising self-rectifying device for power generation from ocean waves; over the past decade, its importance has been rekindled. The bidirectional airflow inside the OWC drives the Wells turbine connected to a generator to harness energy. This study evaluated the aerodynamic performance of two hybrid airfoil (NACA0015 and NACA0025) blade designs with variable chord distribution along the span of a Wells turbine. The present work examines the aerodynamic impact of the variable chord turbine and compares it with one with a constant chord. Ideally, Wells rotor blades with variable chords perform better since they have an even axial velocity distribution on their leading edge. The variable chord rotor blade configurations differ from hub to tip with taper ratios (Chord at Tip/Chord at Hub) of 1.58 and 0.63. The computation is performed in ANSYS™ CFX 2023 R2 by solving three-dimensional, steady-state, incompressible Reynolds Averaged Navier–Stokes (RANS) equations coupled with a k-ω Shear Stress Transport (SST) turbulence model in a non-inertial reference frame rotating with the turbine. The accuracy of the numerical results was achieved by performing a grid independence study. A refined mesh showed good agreement with the available experimental and numerical data in terms of efficiency, torque, and pressure drop at different flow coefficients. A variable chord Wells turbine with a taper ratio of 1.58 had a peak efficiency of 59.6%, as opposed to the one with a taper ratio of 0.63, which had a peak efficiency of 58.2%; the constant chord Wells turbine only had a peak efficiency of 58.5%. Furthermore, the variable chord rotor with the higher taper ratio had a larger operating range than others. There are significant improvements in the aerodynamic performance of the modified Wells turbine, compared to the conventional Wells turbine, which makes it suitable for wave energy harvesting. The flow field investigation around the turbine blades was conducted and analyzed.

Numerical investigation of the reflection of unsteady decelerating incident shock waves

The incident shock attenuation phenomenon in shock tube has received widespread interest because of its inevitable influence on experimental gas properties. However, few studies have investigated the cascading effects of the resulting nonuniformity on shock reflection in shock tunnels before the nozzle. This paper describes a numerical study on the unsteady reflection of a decelerating incident shock driven by a decelerating piston, as a simplification of the complex nonideal factors. The initial decay and uniform parameter distributions are generated based on the non-inertial frame. The results indicate that the existence of the nonuniform area forces the reflected shock wave region to undergo a transition process of attenuation and then stability. The final values of the gas parameters in zone 5 will, therefore, deviate from those given by the traditional relation for an ideal shock tube, which are only dependent on the terminal shock Mach number. This affects the determination of the total temperature T5, which is difficult to measure directly. We discuss the reconstruction of the nonuniform region with the attenuation trajectory of the incident shock wave and find that there is no one-to-one correspondence between this trajectory and the resulting nonuniformity, which introduces additional uncertainties to the predictions. Thus, an analogy method is developed through the multilevel block building algorithm, allowing the total temperature T5 to be determined using the total pressure p5 considering the effect of nonuniformity. Further assessments verify the applicability of this method in cases with multidimensional and viscous interactions.

Precession of planets' orbits between Newtonian gravity and Einstein's general relativity

The recent result that, contrary to a longstanding conviction older than 160 years, the precession of Mercury perihelion can be achieved in Newtonian gravity with a very high precision by correctly analyzing the situation without neglecting Mercury's mass is confirmed. Orbit's precession does not occur in an inertial (in Newtonian sense) frame of reference, but it occurs in the non-inertial frame of reference of the Sun because in Newtonian theory, the distance which is travelled by a body depends on the frame of reference in which the motion of the body is analyzed. After reviewing a previous solution, the precession is directly obtained from the orbit equation in the non-inertial frame of reference of the Sun. The Newtonian formula of the precession of planets' perihelion breaks down for the other planets because the predicted Newtonian result is indeed too large for Venus and Earth. In a previous paper, it was shown that corrections due to gravitational and rotational time dilation, in an intermediate framework (a particular post-Newtonian approximation of general relativity) which analyzes gravity between Newton and Einstein, solve the problem in accordance with some other results in the literature. By adding such corrections, a result consistent with the one of general relativity was indeed obtained. Those corrections also are re-analyzed in this paper by stressing the difference between general relativity and Newtonian physics by evoking the Einstein Equivalence Principle, and the third postulate of relativity. This framework of gravity between Newton and Einstein seems consistent with global covariance. Finally, it is important to stress that a better understanding of gravitational effects in an intermediate framework between Newtonian theory and general relativity, which is one of the goals of this paper, could, in principle, be crucial for a better understanding of the famous Dark Matter and Dark Energy problems.

Schwinger correlation of Dirac fields in accelerated frames

We study the Schwinger correlation of Dirac fields in the noninertial frames under the influences of both constant and pulsed electric fields. We use both the entanglement negativity and quantum mutual information between particle and antiparticle as the indicator of the Schwinger correlation observed by the accelerated observers. We find that the Schwinger correlation in the inertial frames is the largest. With the increase of acceleration of the observers, the Schwinger correlation becomes smaller and smaller, but does not vanish in the limit of infinite acceleration. For the given acceleration, the Schwinger correlation is a nonmonotonic function of the electric field intensity, and there is an optimal value of electric field intensity for which the Schwinger correlation is the largest. In the case of pulsed electric fields, the Schwinger correlation is also the nonmonotonic function of pulsed width, which suggests the existence of optimal pulsed width for observing Schwinger correlation.

Non-inertial interpretation of the Dirac oscillator

Non-inertial physics is seldom considered in quantum mechanics and this contrasts with the ubiquity of non-inertial reference frames. Here, we show an application to the Dirac oscillator which provides a fundamental model of relativistic quantum mechanics. The model emerges from a term linearly dependent on spatial coordinates added to the momentum of the free-particle Dirac Hamiltonian. The definition generates peculiar features (mutating vacuum energy, non-Hermitian momentum, accidental degeneracies of the spectrum, etc). We interpret these anomalies in terms of inertial effects. The demonstration is based on the decoupling of the Dirac equation from the stereographic projection that maps the 3D geometry of the dynamical problem to the complex plane. The decoupling shows that the fundamental mechanical model underpinning the Dirac oscillator reduces to the representation of the oscillator in the rotating reference frame attached to the orbital angular momentum. The resulting Coriolis-like contribution to the Hamiltonian accounts for the peculiarities of the model (mutating vacuum energy, form of the non-minimal correction to the momentum, classical intrinsic spin and gain of its quantum value, accidental degeneracies of the energy spectrum, supersymmetric potential). The suggested interpretation has an interdisciplinary character where stereographic geometry, classical physics of the Coriolis effect and quantum physics of Dirac particles contribute to the definition of one of the few exactly soluble models of relativistic quantum mechanics.

Pairwise interaction of spherical particles aligned in high-frequency oscillatory flow

We present a systematic simulation campaign to investigate the pairwise interaction of two mobile, monodisperse particles submerged in a viscous fluid and subjected to monochromatic oscillating flows. To this end, we employ the immersed boundary method to geometrically resolve the flow around the two particles in a non-inertial reference frame. We neglect gravity to focus on fluid–particle interactions associated with particle inertia and consider particles of three different density ratios aligned along the axis of oscillation. We systematically vary the initial particle distance and the frequency based on which the particles show either attractive or repulsive behaviour by approaching or moving away from each other, respectively. This behaviour is consistently confirmed for the three density ratios investigated, although particle inertia dictates the overall magnitude of the particle dynamics. Based on this, threshold conditions for the transition from attraction to repulsion are introduced that obey the same power law for all density ratios investigated. We furthermore analyse the flow patterns by suitable averaging and decomposition of the flow fields and find competing effects of the vorticity induced by the fluid–particle interactions. Based on these flow patterns, we derive a circulation-based criterion that provides a quantitative measure to categorize the different cases. It is shown that such a criterion provides a consistent measure to distinguish the attractive and repulsive arrangements.

Introducing General Relativity in High Schools: a proposal for a Teaching-Learning Module

A teaching-learning module, aimed at introducing basic concepts of general relativity at the high school level, is proposed. Emphasis is on conceptual rather than technical aspects, and only familiarity with simple calculus is required on the mathematical side. The starting point is a critical overview of the principles of Newtonian mechanics, in particular the role of fictitious forces, as well as of the limits of special relativity. Part of the module is devoted to the discussion and the reproduction of key thought or real experiments, for example experiments involving non-inertial frames, or the Einstein elevator.

Relativistic acceleration in noninertial frames of a line of objects

A general solution to the problem of relativistic acceleration of point objects in the noninertial frame of any of the objects is given in one spatial dimension. The objects are initially at rest in a common inertial frame and accelerate until they are at rest in a second inertial frame. The starting time and position of each object, the acceleration rate of each object, and the number of objects are arbitrary. The solution gives the position and velocity of each object in the noninertial frame of the host object, and the proper time of each, as functions of the proper time of the host. The method is based on system states for a pair of objects, and it is found that there are nine series of states which cover all cases, including those in which objects are separated from the host by its Rindler horizon. The familiar problems of acceleration of an elastic rod and a (Born) rigid rod are treated, and a number of examples are given of spaceflight sequences for multiple craft in tandem.

Theoretical and experimental study on the dynamic behavior of spur gear transmission system during hovering maneuver flights

Gear transmission systems, a crucial component of aircraft power transmission, are subjected to time-varying additional inertial forces and gyroscopic moments in noninertial frame environments when the aircraft performs maneuvering flight actions. In this study, a noninertial frame dynamic model of the gear transmission system during hovering maneuver flights was established, and the accuracy of the theoretical model was verified through conducting hovering maneuver flight simulation experiments. The dynamic behavior of the gear transmission system housing, bearings, and shafts under different hovering maneuver flight parameters was studied. The findings reveal that the maneuvering acceleration of the carrier causes varying degrees of change in the vibration acceleration of the housing, the center distance of the gear pair, the bearing force, and the bending deformation of the shafts, among which the magnitude and direction of the radial bearing force and shaft bending deformation are significantly affected by the maneuvering acceleration. Moreover, the risk of failure can be mitigated through the adjustment of the inclination angle to minimize the bending deformation of the fragile shaft resulting from maneuvering acceleration.

GINGERINO: a high sensitivity ring laser gyroscope for fundamental and quantum physics investigation

Ring Laser Gyroscopes, based on the Sagnac effect, are currently the most sensitive rotation sensors. GINGERINO, a RLG installed underground, shows a proved sensitivity that enters the few frad/s regime in about 2.5 days of integration time. On one hand, this sensitivity is well below the shot–noise–level as predicted applying to GINGERINO the so called independent beam model. On the other hand, it paves the way to the use of RLG in fundamental and quantum physics research. Indeed, high sensitivity rotation measurement opens to test general relativity and alternative theory of gravity. Moreover, it make possible to study the interplay between quantum effects in the optical domain and non-inertial reference frames.

Aerodynamic force by Lamb vector integrals in unsteady compressible flows

PurposeThis study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.Design/methodology/approachExact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).FindingsTwo total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.Originality/valueNo thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

Quantum conditional mutual information of W state in non-inertial frames

Quantum conditional mutual information (QCMI) is a versatile information theoretic measure. It is used to find the amount of correlations between two qubits from the perspective of a third qubit. In this work, we characterise the QCMI of tripartite W-states when some of the qubits are in accelerated motion. Here for our investigations we consider a massless fermionic field in the single-mode approximation. We consider all possible situations with respect to the acceleration of the qubits. From our results, we observe that QCMI can either increase or decrease depending on the role of the qubit being accelerated. Finally we discuss the connection between QCMI and correlations by studying the biseparable and separable states.

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.

Leader-follower formation control based on non-inertial frames for non-holonomic mobile robots.

A chain formation strategy based on mobile frames for a set of n differential drive mobile robots is presented. Considering two consecutive robots in the formation, robots Ri and Ri+1. It is intended that robot Ri+1 follows the delayed trajectory, τ units of time, of the leader robot Ri. In this way, the follower robot Ri+1 becomes the leader robot for robot Ri+ 2 in the formation and so on. With this formation policy, the trailing distance between two consecutive robots varies accordingly to the velocity of the Ri leader robot. Mobile frames are located on the body of the vehicles, in such a way that the position of robot Ri is determined with respect to the frame located on Ri+1 robot. The strategy relies on the fact that the general leader robot R1 describes any trajectory generated by bounded linear v1(t) and angular ω1(t) velocities. For the remaining vehicles in the string, the strategy considers a desired trajectory for the follower robot Ri+1 obtained by an estimation of the delayed trajectory of the leader robot Ri. This desired estimated trajectory is obtained under the knowledge of the actual and past input velocities of the Ri robot. To formally prove the convergence of the formation strategy, the equations describing the time variation of the relative posture between any pair of consecutive vehicles in the formation are obtained, and a feedback law based on local measurements is proposed to get the convergence of robot Ri+1 to the delayed trajectory, τ units of time, of the trajectory previously described by robot Ri. Lyapunov techniques are considered for this fact. The effectiveness of the chain formation solution is evaluated by means of numerical simulations and real time experiments showing an adequate convergence.