Inertial Mass Research Articles

Nonrelativistic limits of the Klein-Gordon and Dirac equations in the Amelino-Camelia DSR

This paper is devoted to the study of the nonrelativistic limit of Amelino-Camelia doubly special relativity and the corresponding modified Klein-Gordon and Dirac equations. We show that these equations reduce to the Schrödinger equations for the particle and the antiparticle with different inertial masses, however, their rest masses are the same. M. Coraddu and S. Mignemi have studied the nonrelativistic limit of the Magueijo-Smolin doubly special relativity. We compare their results with our study and show that these two models are reciprocal to each other in the nonrelativistic limit. We find that particle and antiparticle masses can be different. These different masses lead to the CPT violation. Also, we will find an upper limit on the photon mass.

The bismar scale and elastic collisions: a geometrical analogy

Throughout history, scales have served as instrumental tools for quantifying the weight of objects, relying on a comparative assessment against a specified reference weight. Scales featuring uneven arms, such as the bismar scale, have proven particularly adept at gauging masses within a specific range relative to a predetermined reference mass. On the other hand, the kinematics of elastic collisions hinge on the inertial masses of the colliding entities. By observing the aftermath of a collision between a known reference mass and an object of unknown mass, one can deduce the latter’s mass. In this contribution, we highlight a fascinating and clear analogy between these two methodologies. We do so by adapting a geometric approach, initially applicable to the bismar scale, to both non-relativistic and relativistic elastic collisions, encompassing phenomena such as Compton scattering.

Conversion Factors for Physical Property Measurements in different Rest Frames Using a Revised Version of Relativity Theory Based on the Uniform Scaling Method

The history of the development of the Uniform Scaling Method is reviewed. It has its beginning with the Law of Causality and Newton’s First Law of Kinetics (Law of Inertia). On this basis it can be concluded that the rates of clocks do not change spontaneously, i.e. without the application of some external force. Since the ratio Q of the rates of any two such (inertial) clocks must therefore itself be a constant, it follows that whenever they are used to measure a specific time difference between two events, their respective results must always be in the same ratio: Δt’=Δt/Q. This relationship is referred to as Newtonian Simultaneity since it guarantees that if one of the clocks finds that the events occurred simultaneously (Δt’=0), the other must do so as well (Δt=0). A useful way to interpret Q is as a conversion factor between the different units of time employed in the two rest frames. If we assume that the value of the speed of light is the same in both rest frames, it follows that they must agree on the unit of speed, i.e. the conversion factor in this case is unity (Q0 ). It therefore follows that the conversion factor for the unit of distance must be exactly the same as that for time, namely also Q. This claim of the Uniform Scaling Method is thus seen to be in direct contradiction to the length contraction tenet of Einstein’s theory of relativity introduced in 1905. Experiments with accelerated electrons carried out by Bucherer in 1909 indicate that their inertial mass increase in direct proportion to γ (v) = (1-v2 c-2)-0.5 (v is the speed of the electrons and c = 299792458 ms-1 is the speed of light in free space), the same ratio as observed for the periods of atomic lines by Ives and Stilwell in 1938. Consistency therefore requires that the conversion factor for inertial mass is the same (Q) as for time. Since inertial mass, time and distance are the three fundamental quantities on which all other physical properties are defined (mks system), it follows that the conversion factor for any other property must be an integral multiple of Q. An analogous set of definitions can also be justified for the corresponding conversion factors in the same two rest frames caused by gravitational effects. In this case the conversion factors are always integral multiples of the quantity S, which therefore plays as analogous role as Q in kinetic scaling. Since experiments with circumnavigating atomic clocks carried out in 1971 by Hafele and Keating found that the two types of effects are completely independent of one another, it is therefore useful to define a product Z of the corresponding Q and S factors for each physical property, including those that are used to define the results of electromagnetic measurements. These total conversion factors are stored in Tables 1 and 2 of the manuscript. They are shown to guarantee that if a physical law is valid in one of the rest frames, it will also hold in the other. This relationship allows for an Addendum to Galileo’s Relativity Principle: The laws of physics are the same in all inertial rest frames, but the units in which their results are expressed can differ from one rest frame to another.

Investigating Tailless UAV Flight Dynamics through Modeling, Simulation, and Flight Testing

Tailless Unmanned Aerial Vehicles (UAVs) offer several advantages over their conventional counterparts, including enhanced maneuverability, higher durability, and better stealth. However, they are challenging in their stability and control due to the absence of stabilizing and control surfaces that typically exist in conventional empennage. A crucial process for analyzing the tailless UAVs’ stability/performance characteristics and determining/validating their flight control parameters is done via the modeling and simulation of flight dynamics. This paper presents a comprehensive and systematic procedure for investigating the flight dynamics of a tailless UAV, including modeling, simulation, analytical verification, and flight testing, while also explaining the interconnections among these elements. It also addresses the common challenge of limited accessibility of UAV essential data through using diverse analytical, empirical, and experimental methods. First, a rapid and effective first-principles modeling approach is introduced to simulate the nonlinear six-degree-of-freedom flight dynamics of a small tailless UAV case study. The modeling process follows a modular framework where well-defined experiments and commercial of-the-shelf software, tools, and sensors are employed to build the necessary sub-models, including geometric, mass–inertia, aerodynamic, propulsion, and actuator models. Then, all sub-models are integrated into a simulation environment to allow the prediction of the UAV dynamic response obtained from the given control inputs. The developed flight dynamic model is subjected to a thorough verification process to ensure its integrity and proper functionality by comparing the simulated trim and natural flight modes with the calculated analytical results. Finally, a set of specific flight tests are performed to validate the developed simulation model and verify relevant performance characteristics for the case-study UAV. The results show that the proposed approach provides a systematic and straightforward method for examining the flight dynamics of small tailless UAVs with reasonable accuracy.

Isolating the Contributions from Moments of Inertia in Isotopic Shifts Measured by High-Resolution Cyclic Ion Mobility Separations.

The unexpected finding that isotopomers (i.e., isotopic isomers) can be separated with high-resolution ion mobility spectrometry-mass spectrometry (IMS-MS) has raised new structural considerations affecting an ion's mobility, namely its center of mass (CoM) and moments of inertia (MoI). Unfortunately, thus far, no studies have attempted to experimentally isolate either CoM or MoI, as they are intrinsically linked by their definitions, where MoI is calculated in relation to CoM. In this study, we designed and synthesized four isotopically labeled tetrapropylammonium (TAA3) ions, each with a unique mass distribution. Three of the synthesized TAA3 ions were labeled symmetrically, thus having identical CoM but differing MoI, which we verified using density functional theory (DFT) calculations. Consequently, we were able to isolate the effect of MoI changes in high-resolution IMS-MS separations. Cyclic ion mobility spectrometry-mass spectrometry (cIMS-MS) separations of the isotopically labeled TAA3 variants revealed isotopic mobility shifts attributable solely to changes in MoI. A 60-m cIMS-MS separation demonstrated that two nominally isobaric TAA3 pseudoisotopomers could be partially resolved, showcasing potential feasibility for isotopomer separations on commercially available IMS-MS platforms. With our previously established collision cross section (CCS) calibration protocol, we also quantified the relationship between MoI and CCS. Our results represent the first demonstration of IMS-MS separations based solely on MoI differences. We believe these findings will contribute important evidence to the growing body of literature on the physical nature of isotopic shifts in IMS-MS separations and work toward more accurate CCS predictions.

Reinforcement learning-based moving-target enclosing control for an unmanned surface vehicle in multi-obstacle environments

This paper investigates the moving-target enclosing problem in multi-obstacle environments for an unmanned surface vehicle (USV) with complex unknown factors, including target dynamics, vehicle dynamics, and disturbances. A reinforcement learning-based moving-target enclosing control scheme is proposed to ensure collision-free behavior and bolster the enclosing capability. Specifically, an extended state observer is deployed to estimate the target dynamics. Leveraging the estimated data and control obstacle functions, a virtual safety control law is formulated to dynamically harmonize obstacle avoidance and target enclosing control. Then, a novel controller is constructed to track this control law utilizing a Nussbaum-type function in conjunction with actor–critic neural networks (NNs). The actor and critic NNs are employed to approximate unknown dynamics encapsulating vehicle dynamics and disturbances, and value function, respectively. The Nussbaum-type function is embedded to adaptively identify unknown inertia mass, regulating the control input of the USV with the actor NN online. The proposed scheme effectively decouples obstacle avoidance and target enclosing control and only relies on the measurable variables. A rigorous theoretical analysis is further employed to ensure the closed-loop stability of the USV system. Eventually, Simulations are demonstrated to validate the effectiveness and superiority of the proposed scheme for the USV in multi-obstacle environments.

Strange property of physical quantities of some petal shape objects

We study various physical quantities of objects with petal shapes. N-petal shapes exhibit N-fold rotational symmetry. Furthermore, they might have an additional characteristic: the equation defining their boundaries could be represented by F(N θ). We will show that physical quantities of objects with these characteristics may show strange properties. By ‘physical quantities’, we refer to aspects such as electric potential and electric field due to a charged petal-shaped plate or cylinder on the rotation axis, their mass and moment of inertia. We are going to show that for such objects, these physical observables do not depend on the number of petals, N. This intriguing result has a simple reason.

Development and Analysis of Novel Integrable Nonlinear Dynamical Systems on Quasi-One-Dimensional Lattices. Two-Component Nonlinear System with the On-Site and Spatially Distributed Inertial Mass Parameters

The main principles of developing the evolutionary nonlinear integrable systems on quasi-onedimensional lattices are formulated in clear mathematical and physical terms discarding the whimsical mathematical formulations and computer-addicted presentations. These basic principles are substantiated by the actual development of novel semi-discrete integrable nonlinear system, whose auxiliary spectral and evolutionary operators are given by 4 × 4 square matrices. The procedure of reduction from the prototype nonlinear integrable system with twelve field functions to the physically meaningful nonlinear integrable system with four field functions is described in details prompted by our previous cumulative experience. The obtained ultimate semi-discrete nonlinear integrable system comprises the two subsystems of essentially distinct physical origins. Thus, the first subsystem is the subsystem of the Toda type. It is characterized by the on-site (spatially local) mass parameter and the positively defined elasticity coefficient. In contrast, the second subsystem is characterized by the spatially distributed mass parameters and the negatively defined elasticity coefficient responsible for the low-amplitude instability. We believe our scrupulous consideration of all main steps in developing the semidiscrete nonlinear integrable systems will be useful for the researchers unfamiliar with the numerous stumbling blocks inevitable in such an interesting and prospective scientific field as the theory of semi-discrete nonlinear integrable systems.

Modeling of flexible shaft for robotics applications

Reducing moving mass and effective inertia is essential for achieving safe human–robot collaboration. This can be achieved either by employing remote actuation, which moves the mass of actuators away from the moving elements of the robot, or by elastic actuation, which decouples the inertia of the actuator from the inertia of the robot’s link. Flexible shafts, being torsionally compliant slender long shafts, offer a combination of remote and series elastic actuation over an obstacle. Modeling such transmission is complicated due to its three-dimensional deformation in torsion, bending, and helical buckling. This paper proposes an algorithm for estimating the polar moment of inertia and stiffness of the flexible shafts using their physical dimensions of length and diameter. Using an inertia-spring–damper model, the stiffness parameters are estimated experimentally for nine flexible shafts with variable diameters and lengths in straight and bent configurations. The proposed algorithm is validated with experimental stiffness values for variable diameters and lengths in straight configuration. For bent configuration, an empirical formulation is provided to incorporate the bending deformation effect till a bending angle of 45∘.

The digital twin use for modeling the multi‐storey building response to seismic impacts

AbstractThis work is dedicated to theoretical and experimental research on constructing a digital twin for a 24‐story building located in a seismic zone with the possibility of seismic vibrations of up to eight on the Richter scale. A digital model of the building was developed considering the changes in its geometry (damage or absence of structural elements). This requires detailed field inspections of partially constructed buildings and consideration of the inspection results when constructing a digital model. The boundary conditions, in addition to the geometric characteristics of the building, include the physical and mechanical characteristics of all its structural elements obtained through nondestructive testing methods. Discrepancies between the structural elements' design and actual concrete classes were identified. The initial conditions included real accelerograms at the location of the building, which served as input data for the direct dynamic analysis. Thus, there is a need to develop a hybrid system for modeling the stress–strain state of a 24‐story building that uses information technologies (Internet of Things) with sensors during research. Such an IoT system, combined with one information network using cloud technologies, allows us to obtain the necessary information in real‐time, highlighting the features of the building (the second stage of constructing the digital twin). The bar and spatial models of buildings with distributed parameters of structural stiffness at bending and shear and the mass and mass moment of inertia were considered. The results of numerical studies of the first form of natural vibrations for the building rod (according to the expressions obtained by the authors) and spatial models (performed using the LIRA‐CAD software package developed in Ukraine based on the finite element method) are presented. A comparison with the first experimental form of natural vibrations confirmed that considering the moment of inertia of the building mass makes it possible to determine the ordinates of the self‐form of vibrations and seismic horizontal loads more accurately. The experimental first frequency and form of natural vibrations of a 24‐story residential building in Odesa were obtained from the results of vibration monitoring at the construction stage (16 floors were erected) and after all 24‐floor erection. The direct dynamic method of building calculations for seismic effects specified by earthquake accelerograms was used along with the method proposed by the authors to consider damping during forced building vibration calculations and the actual physical and mechanical characteristics of concrete and reinforcement obtained by non‐destructive testing methods. The calculated vibration amplitudes at the top of the building cantilever model were compared with the damping parameters obtained using the Voicht model and the authors' method under the influence of an accelerogram recorded during the powerful 1977 Bucharest earthquake with an epicenter in the Vrancea area (Romanian Carpathians).

Trajectory dynamics of particles in accelerated toroidal pipe: A computational study using CFD-DPM simulations

In this study, we investigate the behavior of solid particles of varying sizes within an accelerated toroidal filled with fluid using computational fluid dynamics- discrete phase model (CFD-DPM) simulations. A comprehensive grid independence study and validation were conducted to ensure the accuracy of our simulations. We focus on particles with 10-, 50-, and 100-microns diameters. Our simulations indicate that the primary flow (relative tangential velocity) of both the fluid and the particles follow the input acceleration. We also examined the secondary flow within the toroidal. Smaller particles (10 microns) closely follow the fluid flow with minimal lag, while larger particles (50 and 100 microns) exhibit a noticeable lag due to the inertia effect. Furthermore, the displacement from the initial position is also dependent on the particle size, with smaller particles traveling further distances. However, despite the ongoing acceleration of the fluid and the toroidal, the largest particles (100 microns) eventually settle and stop due to their high inertia (mass), and their velocity begins to decrease during the acceleration of the toroidal. These findings highlight the significant role of particle size in determining particle behavior within a toroidal, paving the way for future research and Particle Imaging Velocimetry Gyroscope (PIVG) application.

Finding and analyzing of the energy and force parameters of the flange formation process by orbital stamping by rolling

The study was carried out based on the developed mathematical model of the discrete hydraulic actuator. The model is characterized by considering the nonlinear friction based on the LuGre model, the bidirectional motion of the asymmetric hydraulic cylinder, and the elastic properties of the fluid. A series of simulation experiments on the braking process of the hydraulic actuator in the discrete control mode were carried out. The quantitative relationship between the rod braking time, the maximum peak pressure in the hydraulic cylinder chambers, the value of the initial rod velocity and the inertial mass of the moving parts are determined. Based on the research results it is possible to predict the braking time of the rod and the maximum peak pressure in the hydraulic cylinder chambers under various operating conditions and inertial loads. These predictions can be used in the settings and design process of hydraulic actuators.

Impact of initial slide on downslope seafloor with a weak layer

Submarine landslides are a major offshore geohazard posing increasing threat to offshore and coastal developments. A submarine landslide may usually involve multistage failure triggered by the first failure. During submarine landslide evolution, the emergent sliding mass may act as an impact load on the downslope seafloor potentially leading to surficial erosion of sediments or deeper ploughing failure with the presence of a weak layer. The study presents a comprehensive analysis of seafloor instability and post-failure behaviors subjected to the first slide mass impact, using a large deformation finite element (LDFE) method. Different failure patterns are investigated and the corresponding critical impact loads for triggering the seafloor instability are analyzed. The parameters controlling the strain softening behaviors of soils and the undrained shear strength in the weak layer have significant effects on the critical condition for the seafloor failure. The dynamic inertia of the slide mass, however, has little effect on the results. An empirical equation for assessing the seafloor instability subjected to the first slide impact, with respect to the impact load from the initial slide and the gravity stress relative to the shear strength in the weak layer, is proposed based on a parametric study.

The Synge G-Method: cosmology, wormholes, firewalls, geometry

Unphysical equations of state result from the unrestricted use of the Synge G-trick of running the Einstein field equations backwards; in particular often this results in ρ+p<0 which implies negative inertial mass density, which does not occur in reality. This is the basis of some unphysical spacetime models including phantom energy in cosmology and traversable wormholes. The slogan ‘ER = EPR’ appears to have no basis in physics and is merely the result of vague and unbridled speculation. Wormholes (the ‘ER’ of the slogan) are a mathematical curiosity of general relativity that have little to no application to a description of our Universe. In contrast quantum correlations (the ‘EPR’ of the slogan) are a fundamental property of quantum mechanics that follows from the principle of superposition and is true regardless of the properties of gravity. The speculative line of thought that led to ‘ER = EPR’ is part of a current vogue for anti-geometrical thinking that runs counter to (and threatens to erase) the great geometrical insights of the global structure program of general relativity.

Generation of a substance with negative mass

An analysis of known experiments was carried out to determine the dependence of the mass of electrons on their speed. Errors were discovered in determining the sign of the electron mass. It is shown that at electron velocities above the critical ω = 235696.8871 km/s their masses are negative. The results obtained are explained on the basis of the Principle of Nonequivalence of inertial and gravitational masses since inertial mass can only be positive, and gravitational mass can only be positive or negative The purpose of this work is to show that since radioactive substances can emit electrons with negative mass at velocities above ω, they can be a source of their production.

Research on Inertial Force Attenuation Structure and Semi-Active Control of Regenerative Suspension

To improve the energy recovery ability of the energy-regenerative suspension, a transmission is generally used to increase the motor speed, but this results in a significant increase in the equivalent inertial mass of the suspension. The research on energy-regenerative suspension has been ongoing for more than 20 years, but there have been few product applications, mainly due to the failure to solve the problem of the deterioration of suspension performance caused by equivalent inertial mass. This paper proposes a new suspension configuration with the suspension shock absorber connected to a high-frequency vibration reduction structure and establishes a vibration transmission model. Through frequency domain analysis, it has been conclusively proven that the new-configuration can significantly reduce both the sprung mass acceleration and relative dynamic load of the energy regenerative suspension. On the basis of frequency domain analysis, a scheme based on PWM control of the dissipation resistance value of the energy regenerative suspension is proposed, and through bench comparison experiments, it has been verified that the new-configuration suspension can eliminate the oscillation of the damping force curve of the shock absorber and significantly improve the suspension performance. Further experiments show that using the skyhook semi-active control algorithm the new-configuration suspension can further reduce the sprung mass acceleration and relative dynamic load.

Structural design and dynamic characteristics analysis of braided composite two-stage gear transmission system

In order to realize the lightweight design of the transmission system, the braided composite material is applied to the two-stage gear transmission system. According to the structural characteristics of the two-stage gear reducer box, the whole box is designed to be assembled with the braided base and the box wall. Woven composite materials are applied to the web parts of mixed metal composite gears to realize the design goal of lightweight gears. Then, under the assumption of ignoring the influence of friction, bearings and other factors on the system, the dynamic model of the two-stage gear transmission system considering the box is established. By normalizing and dimensionless processing of the equations, the dimensionless differential equations of motion are obtained. The fourth-order Runge–Kutta method is used to analyze the relationship between the connection parameters and the dynamic characteristics of the system under the two working conditions of rigid and flexible connection between the composite base and the box wall.Through the analytical analysis of vibration displacement of two-stage gear reducer and box, the theoretical basis is found for the numerical analysis results. Finally, the dynamic characteristics of the transmission system are studied by vibration resonance analysis through high and low frequency interference. It is found that in a certain frequency range, with the decrease of the mass and moment of inertia of the transmission parts corresponding to the mixed metal composite gear, the amplitude-frequency characteristic Q of the lightweight gear and gearbox transmission system is slightly lower than that of the common gear and gearbox system, and the stability of the system is increased, and the dynamic characteristics of the system are improved.

When an active bath behaves as an equilibrium one.

Active scalar baths consisting of active Brownian particles are characterized by a non-Gaussian velocity distribution, a kinetic temperature, and a diffusion coefficient that scale with the square of the active velocity v_{0}. While these results hold in overdamped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as ∼v_{0}^{α} with 1<α<2. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibriumlike behavior.

The Coriolis effect and coupled oscillations in a rotating swings amusement ride

Rotating swings are found in many different versions in parks around the world. They are beautiful examples of the equivalence between gravitational and inertial mass: empty swings and swings with heavy adults hang at the same angle to the vertical. However, sometimes one can notice empty swings moving in a different pattern in an outdoor ride, where wind can induce additional motion, sideways or back to front—in addition to any oscillations caused by a tilted carousel head. This paper focuses on oscillations for the simpler case of a non-tilting roof. Even for this case, the oscillating motion is found to be complicated by the Coriolis effect, which leads to a gyroscopic coupling between sideways oscillations and back-to-front oscillations. This coupling is illustrated for a few special cases.

The platform for remote driving of a biomimetic propulsor and measurement of longitudinal and lateral forces generated by the propulsor

The performance characterization of a biomimetic propulsor for a swimming or flying robot typically requires measurement of the longitudinal and lateral forces generated by the propulsion of the propulsor. The propulsor can be either a tail (without or with a peduncle) or a morphing fin (wing), with multiple degrees of freedom (DOFs), and ideally the driving motors are designed to mount outside the propulsor to reduce the mass inertia and moment of inertia of the propulsor. In this article, we design and provide a robust and versatile platform that incorporate the mechanical two-DOFs lever unit and the measurement unit, as well as the configurable driving unit. The two-DOFs lever unit enables the freedoms of the longitudinal and lateral movements but are tightly constrained by the measurement unit that is fixed on the platform carriage for measurement of the longitudinal and lateral forces generated by the propulsor. The driving unit has the motors and the cable-driven modules that are configurable for bidirectional remote actuation, which is plug-and-play and flexible for different types and different numbers of motors. An experiment of the peduncle and the tail for propulsion is illustrated with this platform. The design here also serves as a design guidance for a platform for morphing wings.