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According to Lorentz transformations, for a stationary observer, time in a moving inertial reference frame slows down, while the linear dimensions are reduced. While the first effect was observed more than 80 years ago, the second one has not been directly observed so far. The modified Duguay method is proposed in this paper for measuring the Lorentz contraction of a moving body length using the propagation of light pulses in an optical liquid medium. Three variants of the measurement scheme are considered: with a 'light square' in an optical medium, with a 'light ruler' in two optical media with different refractive indices, and with two relativistic electron bunches in a vacuum. It is shown that the classical effect of compression of spatial intervals between light pulses in an optical medium, which was not considered earlier, considerably reduces the measurement accuracy. It is also shown that the distortion of the sides of a light square oriented orthogonal to the movement direction caused by the different delays of light from different parts of a moving body also reduces the measurement accuracy of the light square method.

Сomprehension of the concepts: «inertial condition of a body» and «inertial force» is the main aim of the article. Authors consider an inertial condition of a body or a system, as independent, autonomous, self-retaining and only internally dialectically changeable condition of the system living under the internal laws.

The mathematical model of nonlinear oscillations of an elastic moving one - dimensional body is investigated. The method of research of the specified model in case of resonant and nonresonant modes of fluctuations is developed. The oscillatory systems considered in the work simulate, in particular, dynamic processes in auger electromechanical machines, technological equipment used in drilling works, etc. The equations in standard form, which determine the parameters of the dynamic process for nonlinear oscillations of a moving body, are considered and investigated. Asymptotic approaches to the study of these mathematical models of oscillations make it possible to obtain and analyze the conditions of resonant and non-resonant modes of operation of the above technological systems.

We show existence and uniqueness of regular time-periodic solutions to the Navier–Stokes problem in the exterior of a rigid body, \(\mathcal B\), that moves by arbitrary (sufficiently smooth) time-periodic translational motion of the same period, provided the size of the data is suitably restricted. Moreover, we characterize the spatial asymptotic behavior of such solutions and prove, in particular, that if \(\mathcal B\) has a nonzero net motion identified by a constant velocity \(\overline {\boldsymbol {\xi }}\) (say), then the solution exhibits a wake-like behavior in the direction \(-\overline {\boldsymbol {\xi }}\) entirely analogous to that of a steady-state flow around a body that moves with velocity \(\overline {\boldsymbol {\xi }}\).

This experimental study examines ventilated supercavity formation in a free-surface bounded environment where a body is in motion and the fluid is at rest. For a given torpedo-shaped body and water depth ($H$), depending on the cavitator diameter ($d_{c}$) and the submergence depth ($h_{s}$), four different cases are investigated according to the blockage ratio ($B=d_{c}/d_{h}$, where$d_{h}$is the hydraulic diameter) and the dimensionless submergence depth ($h^{\ast }=h_{s}/H$). Cases 1–4 are, respectively, no cavitator in fully submerged ($B=0$,$h^{\ast }=0.5$), small blockage in fully submerged ($B=1.5\,\%$,$h^{\ast }=0.5$), small blockage in shallowly submerged ($B=1.5\,\%$,$h^{\ast }=0.17$) and large blockage in fully submerged ($B=3\,\%$,$h^{\ast }=0.5$) cases. In case 1, no supercavitation is observed and only a bubbly flow (B) and a foamy cavity (FC) are observed. In non-zero blockage cases 2–4, various non-bubbly and non-foamy steady states are observed according to the cavitator-diameter-based Froude number ($Fr$), air-entrainment coefficient ($C_{q}$) and the cavitation number ($\unicode[STIX]{x1D70E}_{c}$). The ranges of$Fr$,$C_{q}$and$\unicode[STIX]{x1D70E}_{c}$are$Fr=2.6{-}18.2$,$C_{q}=0{-}6$,$\unicode[STIX]{x1D70E}_{c}=0{-}1$for cases 2 and 3, and$Fr=1.8{-}12.9$,$C_{q}=0{-}1.5$,$\unicode[STIX]{x1D70E}_{c}=0{-}1$for case 4. In cases 2 and 3, a twin-vortex supercavity (TV), a reentrant-jet supercavity (RJ), a half-supercavity with foamy cavity downstream (HSF), B and FC are observed. Supercavities in case 3 are not top–bottom symmetric. In case 4, a half-supercavity with a ring-type vortex shedding downstream (HSV), double-layer supercavities (RJ inside and TV outside (RJTV), TV inside and TV outside (TVTV), RJ inside and RJ outside (RJRJ)), B, FC and TV are observed. The cavitation numbers ($\unicode[STIX]{x1D70E}_{c}$) are approximately 0.9 for the B, FC and HSF, 0.25 for the HSV, and 0.1 for the TV, RJ, RJTV, TVTV and RJRJ supercavities. In cases 2–4, for a given$Fr$, there exists a minimum cavitation number in the formation of a supercavity while the minimum cavitation number decreases as the$Fr$increases. In cases 2 and 3, it is observed that a high$Fr$favours an RJ and a low$Fr$favours a TV. For the RJ supercavities in cases 2 and 3, the cavity width is always larger than the cavity height. In addition, the cavity length, height and width all increase (decrease) as the$\unicode[STIX]{x1D70E}_{c}$decreases (increases). The cavity length in case 3 is smaller than that in case 2. In both cases 2 and 3, the cavity length depends little on the$Fr$. In case 2, the cavity height and width increase as the$Fr$increases. In case 3, the cavity height and width show a weak dependence on the$Fr$. Compared to case 2, for the same$Fr$,$C_{q}$and$\unicode[STIX]{x1D70E}_{c}$, case 4 admits a double-layer supercavity instead of a single-layer supercavity. Connected with this behavioural observation, the body-frontal-area-based drag coefficient for a moving torpedo-shaped body with a supercavity is measured to be approximately 0.11 while that for a cavitator-free moving body without a supercavity is approximately 0.4.

An approximate solution for the steady linear internal wave field generated by a localized, horizontally moving source in a thermocline is derived using ray and WKB (Wentzel–Kramers–Brillouin) theory. The waves are assumed to be steady in a reference frame moving with the source velocity. This solution is shown to agree in the limit of propagating waves with an existing solution that is expressed in terms of an eigenfunction expansion. The WKB method is shown to reproduce all the factors in the eigenfunction solution, not just the eigenfunctions themselves. It also reveals the physical significance of the terms in the eigenfunction solution. Furthermore, the WKB solution suggests an alternate way to compute the wave field numerically that is computationally more efficient.

Thus far in this book, we have focused our attention on two principal aspects of inviscid flow: first, on obtaining the flow field about a moving body amidst a general distribution of vorticity in the surrounding fluid; and second, on computing the resulting fluid dynamic force and moment exerted on the body in this scenario. We have thus far had little to say about the motion of this vorticity. However, our analysis of the problem is incomplete until we have addressed this motion, particularly because—as we found in our discussion of impulse-based calculations in Chap. 6—the force and moment depend on the time rate of change of the vorticity’s distribution.

This paper is devoted to an experimental investigation of the motion of a rigid body set in motion by rotating two unbalanced internal masses. The results of experiments confirming the possibility of motion by this method are presented. The dependence of the parameters of motion on the rotational velocity of internal masses is analyzed. The velocity field of the fluid around the moving body is examined.

A flexible biomimetic fish-like robot for use in a flow in narrow passage was developed. Downsizing of the moving body was achieved using shape memory alloy (SMA) actuators. However, overheating an SMA actuator causes phase-transition saturation, and may cause a decrease in the fin vibration amplitude. In order to avoid this problem, a new driving method that utilized a self-excited oscillator was introduced. This proposed method is suited for generating oscillation with keeping temperature in SMA constant by using self-sensing, and needs to adjust only one parameter. We confirmed the effectiveness of the proposed driving method against overheating based on experiments and numerical simulations. Simulation proved that this method can keep thrust force of the moving body constant. For the fish-like moving body, multiple actuators are needed to realize higher degree of freedom behavior, and the phases of these actuator outputs also are needed to be synchronized to generate fish-like behavior, i.e., traveling wave. On the other hand, in the proposed driving method, the actuator system simulates a self-excited vibration system. Therefore, it was necessary to design the coupled inputs for oscillators composed by actuators to synchronize the oscillator outputs. To achieve this, a phase model was obtained from an actuator model, which consists of a thermal conductivity model and hysteresis model using a phase reduction analysis. Coupled inputs for proposed connecting method were designed based on this phase model, and the relationship between the phase difference of the coupled actuators and the connection gains was examined. Finally, we realized phase control using this.

The results of numerical study of the detonation initiation by small diameter spherical supersonic projectile in reacting mixture are presented. A stoichiometric hydrogen and oxygen mixture diluted with argon was used as a reacting medium. The reduced kinetic scheme of chemical reactions was used in our study. The flow regimes and the detonation cell size obtained numerically and experimentally were compared and showed good agreement. Calculations for various sphere diameters at fixed pressure were carried out. The detonation initiation energy for the calculated data was estimated.

The problem of choosing an optimal strategy for moving in the rain has attracted considerable attention among physicists and other scientists. Taking a novel approach, this paper shows, by studying simple shaped bodies, that the answer depends on the shape and orientation of the moving body and on wind direction and intensity. For different body shapes, the best strategy may be different: in some cases, it is best to run as fast as possible, while in some others there is an optimal speed.

Air flow electrization induced by the motion of bodies made of different materials is studied experimentally by detecting a potential appearing at an annular antenna through which the body passes. It is found that the motion of the body is accompanied by the motion of two unlike charges. The positions of the charges relative to the moving body versus its length are determined. Some parameters influencing the value of the charges are considered. It is shown that the kinematics of the body can be determined by recording an electric field accompanying its motion.

This paper pertains to the observations of the sliding friction force from different moving bodies. The paper derives the equations required to predict the forces on the free-body diagrams of two sliding bodies when observed from a third moving body. The force equations were determined with the application of virtual work to determine system equilibrium. The results show that any sliding force equation including the classical Newtonian tractive equation must be multiplied by an intrinsic theoretical equation to obtain equilibrium on the isolated body when observed from a third moving body. This intrinsic equation is defined as the instantaneous percent sliding of the contact.

Volume perception, that is, perception of a partially enclosed space filled with a medium, can be assessed not only from binocular viewing but also from motion. We studied the volume perception of a cylindrical object in motion. The motion (rotation, translation, or rolling) of the cylindrical object was simulated with and without appearing and disappearing parts (ADPs). We found that volume perception could be assessed easily with ADPs but was difficult without ADPs. These experimental results indicate that ADPs are an essential factor for volume perception from motion, which is correspond to binocularly unpaired regions for volume perception in binocular viewing.

A finite-volume model for the gas flow in a compressible flow driven system with two moving components is developed and applied. In this system, high pressure and temperature compressible flow propels one body along a main flow channel. When this body passes an opening in the main flow channel, some of the high pressure gas bleeds off, entering a secondary, telescoping, flow channel that empties into a plenum. The bleed-off flow causes the pressure in the plenum to increase, actuating the motion of a secondary (actuated) body that forms a bounding surface of the plenum, causing the plenum to expand and the secondary channel to lengthen. This model is used to characterize the basic flow effects in the system and to investigate the significance of the system parameters. For the parameters studied, the flow in the system consists of a series of pressure pulses rather than a continuous flow, with reflected pressure waves playing a significant role in the flow field development. For a given initial pressure, changing the size of the opening and secondary flow channel had a minimal effect on the motion of the propelled body. The size of the opening and the initial high pressure were found to have the greatest impact on the velocity of the secondary, actuated moving body.

In order to increase more greatly the measurement accuracy for the laser tracking system in measuring the moving body, a laser beat-wave interferometry method is approached based on the absolute measuring distance. The He – Ne laser with the two hot steady frequency modes is used as the light source for the laser tracking system. The light source developed by us not only has the advantages of steady frequency, high precision and strongly anti-interference capability, but also it mainly has the same character in the shoot stability degrees and laser frequency stability degrees. By using the laser beat-wave interferometry method, we can realize the absolute distance measurement of the moving body, and the laser tracking system has very high measurement precision, fast tracking speed and anti-interference capability.

This paper depicts a ghost cell method to solve the three dimensional compressible time-dependent Euler equations using Cartesian grids for static or moving bodies. In this method, there is no need for special treatment corresponding to cut cells, which complicate other Cartesian mesh methods, and the method avoids the small cell problem. As an application, we present some numerical results for a special moving body using this method, which demonstrates the efficiency of the proposed method.

A theoretical model for interaction of a submerged moving body with the conjugate flow in a three-layer fluid is proposed to depict the internal flat solitary wave, which is observed in experiments conducted by the present authors. A set of coupled nonlinear algebraic equations is derived for the interfacial displacements. The numerical results indicate that (a) the conjugate flow due to a two-dimensional body moving at the bottom possesses an apparent behaviour with two convex interfaces; (b) the solution satisfying the existence criterion is always unique near the relatively stable state of system. Theoretical analysis is qualitatively consistent with the experimental results obtained.

Special method is presented for treatment of moving periodic structure. The analyzing of the simplest model reveals the speed-dependent diffraction anomalies. This physical effect only occurs under the slow-wave driving and when transverse resonance condition satisfied. The theory and the results may have significance in interdisciplinary fields associated with moving periodic structure.

The course of a peritrichous bacterium such as E. coli crucially depends on the level of synchronization and self-organization of several rotating flagella. However, the rotation of each flagellum generates counter body movements which in turn affect the flagellar dynamics. Using a detailed numerical model of an E. coli, we demonstrate that flagellar entanglement, besides fluid flow relative to the moving body, dramatically changes the dynamics of flagella from that compared to anchored flagella. In particular, bundle formation occurs through a zipping motion in a remarkably rapid time, affected little by initial flagellar orientation. A simplified analytical model supports our observations. Finally, we illustrate how entanglement, hydrodynamic interactions, and body movement contribute to zipping and bundling., 5 pages

As stated at the end of Chap. 5, if at large Reynolds numbers a moving body is dressed in fully attached boundary layers, the flow can be solved by potential-flow theory with good accuracy, and then a boundary-layer correction yields the friction force to the body.

Non-steady interactions between plasmas and aircraft in its near wake region are investigated in detail. Under the non-static limit, a set of equations that describe these interactions are obtained. The results of the numerical simulation show that the cavitons of transverse plasmas are excited and density cavitons appear when the envelope of plasma becomes sufficiently intensive. This is very important for detecting the moving body that has a `stealth' characteristic.

Within the framework of the model of local interaction between a moving body and a medium and under the assumption that the tangential stress on the body surface is described by the mixed model of friction, the shapes of the bodies that have a given area of base and afford, for a rectilinear motion in the medium, a minimum to the resistance or a maximum to the length of the trajectory of an inertial motion are found. The parameters of the optimal body shape are related with the medium characteristics and the body velocity.

On observe souvent dans la nature que l'ascension ou la chute d'un corps peut presenter des mouvements oscillatoires (spirale, zigzag) ou plus desordonnes. Nous nous sommes penches sur les causes des instabilites du mouvement d'un corps en ascension sous l'effet de la gravite, dans un fluide au repos. Nous avons conduit une etude experimentale des mouvements oscillatoires de corps legers montant librement dans un fluide peu visqueux. Des resultats originaux concernant la cinematique de cylindres minces sont presentes ici pour une large gamme de nombres d'Archimede (flottabilite sur effets visqueux) et du rapport de forme (diametre sur epaisseur). Nous avons analyse les oscillations de la vitesse et de l'orientation des cylindres (frequences, amplitudes et differences de phases), ce qui a mis en evidence l'effet crucial du rapport de forme dans le couplage entre la translation et la rotation.

The flow-field and the acoustic-field around moving bodies are simulated by the Arbitrary Lagrangian Eulerian formulation in the finite difference lattice Boltzmann method. The validity of the ALE is checked by comparing flow about a square cylinder in ALE formulation and that in the fixed coordinates, and both agree very well. Matching procedure between the moving grid and fixed grid is also considered. The proposed method in which the both grids are connected through buffer region is shown to be superior to moving overlapped grid. Dipole-like emissions of sound wave from harmonically vibrating bodies in two- and three-dimensional cases are simulated. Sound wave emitted from rapidly rotating elliptic cylinder is also successfully simulated.

An asymmetry in Maxwell's electrodynamics concerning the electromagnetic image of a moving spherical conductor is pointed out. The asymmetry, if properly understood, opens the door to special relativity.

This paper presents a dynamic laser speckle method for directly measuring the relative velocity between two contact or adjacent objects. It has been demonstrated that the relative velocity can be determined by the utilisation of interference of the dynamic speckles produced by two moving objects illuminated by one or two laser beam(s). A theoretical analysis unveils the relationship between the relative velocity and the auto-correlation of the photo-current signal produced by a detector. Experiments for verifying the proposed method are carried out and the test results are presented. Further development of the method is also discussed.

The dynamic behavior of a heavy homogeneous ball rolling without slipping in a spherical recess of a translationally moving body is analyzed. The equations of motion of the ball are derived based on Appell's nonholonomic mechanics. The evolution of the dynamic system in time is analyzed numerically.

The subject of this paper is the long-lasting controversy on the relativistic transformation of temperature, generally known as the Planck-Ott imbroglio. Various, mostly unsuccessful, attempts to solve this demanding problem using a combinations of tools of classical thermodynamics, transformation rules of special theory of relativity, theory of black-body radiation and kinetic theory, are reviewed. Using phenomenological analysis, we demonstrate that the failure of these attempts and the existence of the imbroglio itself are most likely due to the misunderstanding of the physical meaning of temperature and to some serious flaws in foundations of classical thermodynamics. We further show that the temperature of a moving body must remain invariant for observers in all relatively moving frames.

We calculate the time delay of light in the gravitational field of a slowly moving body with arbitrary multipoles (mass and spin multipole moments) by the Time-Transfer-Function (TTF) formalism. The parameters we use, first introduced by Kopeikin for a gravitational source at rest, make the integration of the TTF very elegant and simple. Results completely coincide with expressions from the literature. The results for a moving body (with constant velocity) with complete multipole-structure are new, according to our knowledge., Comment: 9 pages, no figures

Effects of a diffuser on the spectral degree of coherence and on the spectrum of light produced by transmitting light through the diffuser are described. Both stationary and uniformly moving diffusers are considered and the analysis applies to dielectric as well as to absorbing diffusers. The results are illustrated by numerical examples.

An experimental study was conducted to investigate the water entry phenomenon. A facility was designed to carry out the tests with the entry velocities of around 352 m/s. Visualization, pressure measurement, velocity measurement and underwater impact test were performed to investigate the hydroballistic behavior of the underwater moving body, the underwater flow field, the supercavitation, etc.. This study shows that the motion of a high-speed underwater body is strongly three-dimensional and chaotic. Furthermore, it is found that the distribution of the trajectory deflection of the underwater projectile depends on the depth of water. It is also found by measuring the deformation on a witness plate submerged in water, that the impact energy of an underwater projectile is reduced as it penetrates deeper into water.

We describe a speckle interferometer system that uses two orthogonally polarized reference beams in phase quadrature to distinguish the direction of motion of an optically rough, moving body.

In interferometry, spatial heterodyning is performed by multiplying the optical phase to be determined by a reference phase. Thus the spatial frequency spectrum corresponding to the signal investigated is better identified and manipulated. We propose a holographic interferometry method that is spatially heterodyned by deliberate rigid-body movement of the object investigated. The object deformation is calculated from the fringe pattern corresponding to two different positions of the object. This work is aimed at a quantitative deformation analysis of highly dynamic objects through pulsed holographic interferometry. En interferometrie, l'heterodynage spatial consiste a multiplier la phase a determiner par une phase de reference afin de mieux reconnaitre dans le spectre de Fourier le domaine de frequences spatiales constituant le signal. Cet artifice permet d'effectuer convenablement les operations de filtrage de frequence, apres quoi il ne reste plus qu'a reconstruire numeriquement le signal d'origine a l'aide d'un algorithme simple. Nous presentons une technique d'interferometrie holographique ou l'heterodynage spatial est obtenu grâce au deplacement (delibere ou spontane) de l'objet. Les deformations de cet objet peuvent alors etre reconstituees a partir de l'interferogramme correspondant a deux positions de celui-ci. Le but de ce travail est l'analyse des deformations des objets en mouvement rapide par interferometrie holographique pulsee.

Resume Le developpement du transfert de chaleur ainsi que celui de l'ecoulement bidimensionnel incompressible d'un fluide visqueux, autour d'un cylindre circulaire mis brusquement en mouvement rectilineaire sont etudies pour une large gamme de nombres de Reynolds ( Re = 550–9500). L'equation de transport de la vorticite et l'equation de l'energie sont resolues en utilisant une methode de differences finies de second ordre dans les deux directions du domaine. L'equation de Poisson pour les lignes de courant, est resolue par une methode Fourier-Galerkin dans la direction de l'ecoulement, que nous considerons symetrique, et une methode de differences finies de second ordre dans la direction radiale. L'avance temporelle est faite en utilisant un schema d'Adams-Bashforth de second ordre pour Re = 550–3000 et une methode Runge-Kutta de quatrieme ordre pour Re superieur a 3000. Les resultats numeriques sont qualitativement compares avec des resultats experimentaux et numeriques publies precedemment dans le cas particulier du cylindre indeformable. La comparaison est satisfaisante.

This paper is an attempt to give a concise presentation of the main concepts of continuum mechanics and to show their articulation. Functional definitions have been favoured.The first section is devoted to a review of continuum mechanics.The second section deals with the mechanics of materials.Constitutive equations of the material are given first by equations of state and then by complementary equations written in order to fulfil the fundamental inequality concerning the production of entropy and the physical properties of the material (viscosity, plasticity, damage etc.).Section 3 gives the Lagrangian and the Hamiltonian formulations for a moving body. Section 4 is devoted to the motion of surfaces through which discontinuities appear, to show briefly two examples of application of the previous concepts. One can easily define the source of intrinsic inhomogeneity, of heat, of irreversible entropy on a surface of phase transition and also for a shockwave. SommarioIn questo lavoro si cerca di dare una presentazione concisa dei concetti fondamentali della meccanica dei continui e di mostrare le loro articolazioni,con particolare rilievo alle definizioni funzionali. La prima sezione e dedicata ad un esame generale introduttivo. La seconda alla meccanica dei materiali, le cui equazioni costitutive sono date come equazioni di stato e come equazioni complementari scritte al fine di soddisfare le diseguaglianze concernenti la produzionedi entropia e le proprieta fisiche dei materiali (qualiviscosita, plasticita, guasti...).La terza sezione da le formulazioni Lagrangiana ed Hamiltoniana per il moto di un corpo.La quarta sezione e dedicata al moto di superfici di discontinuita per mostrare brevemente due esempi di applicazione dei concetti precedenti.Viene quindi definita la sorgente di disomogeneita intrinseca, di calore, di entropia irreversibile su di una superficie, di transizione di fase ed anche di un' onda d'urto.

In this work the structure method is applied for establishing the vibration equations of beam under the action of some moving body. An algorithm is build to solve the vibration equations of the considerable system. From this algorithm a computer program is set up with TURBO PASCAL 6.0 language.

In this text the method of substructures [2] is applied for establishing the vibration equation of beam under the action of moving body. Later an algorithm is built to solve the vibration equation received. From this algorithm a computer program is set up with TURBO PASCAL 6.0 language.

In 1989 Supplee described an apparent relativistic paradox on which a submarine seems to sink to observers at rest within the ocean, but it rather seems to float in the submarine proper frame. In this letter, we show that the paradox arises from a misuse of the Archimedes principle in the relativistic case. Considering first the special relativity, we show that any relativistic force field can be written in the Lorentz form, so that it can always be decomposed into a \emph{static} (electric-like) and a \emph{dynamic} (magnetic-like) part. These gravitomagnetic effects provide a relativistic formulation of Archimedes principle, from which the paradox is explained. Besides, if the curved spacetime on the vicinity of the Earth is taken into account, we show that the gravitational force exerted by Earth on a moving body must increase with the speed of the body. The submarine paradox is then analyzed again with this speed-dependent gravitational force., Comment: Final version. 7 pages, 2 figures, Keywords: Supplee's submarine paradox, theory of relativity, gravitomagnetism, Archimedes principle, Lorentz force