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

Context. Radial differential rotation is an important factor in stellar dynamo theory. In the Sun, helioseismology has revealed a near-surface shear layer in the upper 5–10 percent of the convection zone. At low to midlatitudes, the rotation velocity gradient decreases sharply near the surface. A depth gradient in rotational velocity was recently detected in the low photosphere using a differential interferometric method on spectroscopic data. Granular structures at different depths in the Fe I 630.15 nm line showed a systematic retrograde shift compared to continuum structures, which suggests a height-related decrease in angular velocity. This estimate depends on the assumed granulation coherence time. Aims. We use a more direct approach to measure the differential rotational velocity at different photospheric heights. Methods. We performed spectroscopic scans of the same granular region in Fe I 630.15 nm and Ca I 616.2 nm lines, and measured displacements of images at different line chords between consecutive scans. These observations require excellent seeing, stable adaptive optics correction, and scanning times shorter than the granulation lifetime. Adaptive optics stabilizes continuum images but not higher-altitude rotation differences. We used both THEMIS and HINODE Solar Optical Telescope Fe I 630.15 nm data to measure formation height differences via perspective shifts observed away from the disk center with the slit radially oriented. Results. Measurements at disk center and ±25° latitude along the central meridian show a parabolic decrease in rotational velocity with height that reaches about 16% slower rotation at 80 km above the continuum. No significant difference is found between equator and ±25° latitudes. Conclusions. The low photosphere is a transition zone between the convective and radiative layers. Our measurements provide new constraints on its dynamical behavior and valuable boundary conditions for numerical simulations of the Sun’s upper convection zone.

The increasing evidence of rotational motions due to earthquakes is now motivating civil engineers to investigate the effects of rotational ground motions on structures. With the advancement in instrumentation techniques, rotational sensors have been developed in the past few years, which can measure three components of rotational waves in addition to the translational waves. Conventionally, buildings are designed to withstand horizontal and vertical translational ground motions to minimize the damage to human life and financial losses during an earthquake. Damage to the structure is identified at two levels; (i) structural and (ii) material. The structural damage in reinforced concrete buildings is visible in the form of cracks and spalling concrete, which reduces the overall load-carrying capacity of the building. The damage at the material level is not visible to the human eye. This damage can be identified using coda wave interferometry techniques. In this method, a high cross-correlation between the coda of two waves passing a point on different days of experiment indicates a negligible change in the shear wave velocity of the material. In comparison, a lower cross-correlation signifies considerable change in the material properties.    In order to understand how rotational motions affect reinforced concrete structures and how these can be simulated, the present work makes a novel attempt to use the newly developed rotation measuring sensors, BlueSeis 3A and IMU50, to understand the damage in a model concrete bridge structure (BLEIB). We employ advanced sensors in addition to conventional broadband and ultrasonic sensors on the 24m long two-span continuous reinforced concrete bridge equipped with various non-destructive sensing techniques and subjected to a variable pre-tension force of up to 450kN and various static loads. As an initial analysis, we first identify the bridge's first three fundamental frequencies and mode shapes from both recorded translational and rotational data. The analysis shows that the same fundamental frequencies are obtained from the recorded translational and rotational data. However, we expect to see a difference in the mode shapes. Theoretically, rotations are maximum at the bridge support and minimum at the centre of the bridge span. This behaviour is the reverse of what we observe from translational motions, where maximum translations are observed at the centre of the span while minimum at the supports. As the study plans to simulate rotational motions for reinforced concrete structures, a finite element model of the prototype bridge is also developed, and the fundamental frequencies and mode shapes of the model are validated with those obtained from the recorded data. This work shall be extended to applying coda wave interferometry to the rotational data recorded on the bridge to understanding the change observed in material properties when the bridge is subjected to active and passive forces.

Traditional research-grade three-component seismic sensors are inherently sensitive to both translational ground motion and rotational (tilt) motion, particularly on the horizontal components. The outputs of traditional seismometers represent a sum of rotation and displacement information. As a result, recorded signals represent a superposition of displacement and rotation, even though most processing and interpretation workflows assume purely translational motion. This limitation becomes increasingly important for applications involving near-field ground motion, ground-structure interaction, and structural response monitoring, where rotational effects can significantly influence observed building and infrastructure dynamics. Recent advances in sensor technology are now allowing accurate and precise discrimination between translational and rotational motion. Stratis is the world’s first integrated seismic sensor to provide simultaneous, co-located measurements of all six degrees of freedom, delivering concurrent velocity (m/s) and rotational velocity (rad/s) outputs in the Z, N, and E directions. By measuring all six degrees of freedom at a single point, Stratis avoids the spatial differencing and approximation errors associated with multi-instrument rotational estimates. The availability of co-located rotational measurements enables correction for tilt-induced contamination in translational records, supporting the derivation of rotation-corrected displacement signals and improving the fidelity of ground motion and structural response observations. By integrating rotational and translational sensing into a single compact instrument, the installation process is also greatly simplified, thereby enabling wider access to rotational seismic data. This supports interdisciplinary applications spanning seismology, structural engineering, and seismic risk mitigation, including post-event damage assessment, long-term monitoring of structural health, and improved characterization of earthquake ground motion relevant to robust infrastructure design.

Precision measurement of segmental motion from flexion—extension radiographs of the lumbar spine

Two explosions were set off on 4 March 2008 at the N3 explosion site in northeastern Taiwan. The code name for the first shot with 3000 kg explosives is N3P and that for the second shot with 750 kg explosives is N3. To record these two explosions, 8 triaxial rotational sensors, 13 triaxial accelerometers, and 12 six-channel, 24 bit dataloggers with Global Positioning System receivers were deployed to continuously record several hours before and after the explosions. These instruments were installed at about 250 m (1 station), 500 m (11 stations), and 600 m (1 station) from the explosions. The 11 stations form a center array with station spacing of about 5 m. Except for one rotational sensor, onscale records were obtained. Although the N3P shot used four times larger amounts of explosives than those used for the N3 shot, the peak ground translational acceleration and rotational velocity at the 13 station sites from the N3P shot are only about 1.5 times larger than those for the N3 shot. We also observed large variations (by tens of percent) of translational accelerations and rotational velocities at the center array with station spacing of about 5 m. The largest peak rotational velocity was observed for the x component: 2.74 and 1.75 mrad/sec at a distance of 254 m from the N3P and N3 shots, respectively. The main purpose of this article is to document our recordings of rotational and translation motions from two explosions in Taiwan and to release the data online for open access. The translational acceleration data from this experiment have been analyzed by Langston et al. (2009), and we plan to submit an article with analysis of the rotational velocity data in the future.

This paper addresses the problem of estimating, analyzing and tracking objects moving with spatio-temporal rotational motion (spin or orbit). It is assumed that the digital signals of interest are acquired from a camera and structured as digital image sequences. The trajectories in the signal are two-dimensional spatial projections in time of motion taking place in a three-dimensional space. The purpose of this work is to focus on the rotational motion, i.e. estimate the angular velocity. In natural scenes, rotational motion usually composes with translational or accelerated motion on a trajectory. This paper shows that trajectory parameters and rotational motion can be efficiently estimated and tracked either simultaneously or separately. The final goal of this work is to provide selective reconstructions of moving objects of interest. This paper constructs new continuous wavelet transforms that can be tuned to both translational and rotational motion. The parameters of analysis that are taken into account in these rotational wavelet transforms are space and time position, velocity, spatial scale, angular orientation and angular velocity. The continuous wavelet functions are finally discretized for signal processing. The link between rotational motion, symmetry and critical sampling is also presented. Applications are presented with tracking and estimation.

Molecular dynamics studies of two generalized forms of the rough sphere model are reported. The generalization permits us to vary the coupling between rotational and translational motion through a stick parameter λ. The autocorrelation functions show deviations from the Enskog theory for all values of λ studied—indicating that collective effects are involved. It appears that the angular velocity correlation function is the sum of two exponentials. A simulation of a mixture of disparate sized rough spheres was also performed. It is found that the rotational motion of the small particle is not significantly altered upon introduction of the large particles, but the linear velocity correlation function of the small particle differes considerably from that of the neat fluid (in the time regime from 5–15 mean collision time units).

When whole-body is exposed to vertical vibration, asymmetry shape of human body affects the response on the translational(fore-aft, lateral, vertical) and rotational(roll, pitch, yaw) motion. While the translational motion has been studied with various titles, it has been rare to study the rotational motion of human body exposed to vertical excitation because of lack of experimental equipment. This study was performed by using a 6-axis force plate installing strain gage type sensors for the rotational response. Sixteen male subjects were exposed to vertical vibration on rigid seat in order to investigate apparent mass of three translational motion and apparent eccentric mass of three rotational motion. Random signal was generated to make excitation vibration which was on an effective frequency range of 3~40 Hz, and magnitude of 0.224 m/<TEX>$s^2$</TEX> r.m.s. The frequency range and magnitude used was selected for the vibration of passenger vehicle on idling condition. As the result, cross-axis apparent masses of fore-and-aft and lateral direction were not significant showing 20 % and 3 % of vertical apparent mass relatively. And apparent eccentric mass of pitch motion was dominant when compared to that of roll and yaw motion, which is reasoned by asymmetry direction of human body sitting on a seat.

BackgroundDuring prostate stereotactic body radiation therapy (SBRT), prostate tumor translational motion may deteriorate the planned dose distribution. Most of the major advances in motion management to date have focused on correcting this one aspect of the tumor motion, translation. However, large prostate rotation up to 30° has been measured. As the technological innovation evolves toward delivering increasingly precise radiotherapy, it is important to quantify the clinical benefit of translational and rotational motion correction over translational motion correction alone.PurposeThe purpose of this work was to quantify the dosimetric impact of intrafractional dynamic rotation of the prostate measured with a six degrees‐of‐freedom tumor motion monitoring technology.MethodsThe delivered dose was reconstructed including (a) translational and rotational motion and (b) only translational motion of the tumor for 32 prostate cancer patients recruited on a 5‐fraction prostate SBRT clinical trial. Patients on the trial received 7.25 Gy in a treatment fraction. A 5 mm clinical target volume (CTV) to planning target volume (PTV) margin was applied in all directions except the posterior direction where a 3 mm expansion was used. Prostate intrafractional translational motion was managed using a gating strategy, and any translation above the gating threshold was corrected by applying an equivalent couch shift. The residual translational motion is denoted as Tres. Prostate intrafractional rotational motion Runcorr was recorded but not corrected. The dose differences from the planned dose due to Tres + Runcorr, ΔD(Tres + Runcorr) and due to Tres alone, ΔD(Tres), were then determined for CTV D98, PTV D95, bladder V6Gy, and rectum V6Gy. The residual dose error due to uncorrected rotation, Runcorr was then quantified: ΔDResidual = ΔD(Tres + Runcorr) ‐ ΔD(Tres).ResultsFractional data analysis shows that the dose differences from the plan (both ΔD(Tres + Runcorr) and ΔD(Tres)) for CTV D98 was less than 5% in all treatment fractions. ΔD(Tres + Runcorr) was larger than 5% in one fraction for PTV D95, in one fraction for bladder V6Gy, and in five fractions for rectum V6Gy. Uncorrected rotation, Runcorr induced residual dose error, ΔDResidual, resulted in less dose to CTV and PTV in 43% and 59% treatment fractions, respectively, and more dose to bladder and rectum in 51% and 53% treatment fractions, respectively. The cumulative dose over five fractions, ∑D(Tres + Runcorr) and ∑D(Tres), was always within 5% of the planned dose for all four structures for every patient.ConclusionsThe dosimetric impact of tumor rotation on a large prostate cancer patient cohort was quantified in this study. These results suggest that the standard 3–5 mm CTV‐PTV margin was sufficient to account for the intrafraction prostate rotation observed for this cohort of patients, provided an appropriate gating threshold was applied to correct for translational motion. Residual dose errors due to uncorrected prostate rotation were small in magnitude, which may be corrected using different treatment adaptation strategies to further improve the dosimetric accuracy.

SUMMARYA multidimensional positioning mechanism, along with high speed and high accuracy, is essential for an industrial machine. A positioning machine operates precisely in both vertical linear motion (z‐axis) and rotary motion (θ‐axis). A ball screw mechanism is used for thez‐axis whereas a servo motor is used for the θ‐axis. We developed a direct drive θ‐z motor for rotary and linear motion. Torque and thrust are generated directly by the mover. Thus, high speed and high accuracy as well as miniaturization are achieved without using machine elements such as a ball screw and belt. In this paper, we describe the structure and operating principle of the θ‐Z motor, and the sensor that can detect the θ‐axis and thez‐axis position. In addition, we consider a design method that minimizes copper loss by taking advantage of the shape of the permanent magnet and coil. Furthermore, using a prototype we evaluated the characteristics of torque, thrust, and repeatability.

Cable driven parallel robot (CDPR) possesses large workspace, outstanding dynamic performance and high load capacity. However, due to the actuation method of CDPR, only limited motion modes can be achieved, and its rotational and translational motions are usually coupled. This letter presents a novel design of CDPR, through applying winch-integrated driving method and wrapping driving cables around the moving platform, the positions of driving cables' attach points on moving platform adaptively vary with the movement. The proposed CDPR design naturally enables a novel planar one-translational and one-rotational (1R1T) motion mode with decoupled control of translation and rotation. The performance of the design is validated through simulation and experiment, confirming that there are no other motions generated and the translational and rotational motions can be controlled independently. The proposed configuration further expands the motion mode as well as operational capabilities of CDPR.

A video containing multiple objects undergoing independent translational and rotational motions is analyzed through a combination of spatial- and frequency-domain representations. The Fourier transform of the sequence is used to estimate the multiple translations and rotations in a computationally efficient manner, which is also robust to local inaccuracies and global illumination changes. A novel algorithm is presented for the simultaneous extraction of all objects undergoing translation and the background via a least squares technique that takes place entirely in the Fourier domain. Spatial information is combined with the frequency domain object extraction results, to further refine them. For the case of rotational or combined, rotational and translational motions, the moving objects are segmented using purely spatial information. We show that the combined analysis takes advantage of the strengths of both representations, by providing reliable and computationally efficient motion estimates and object segmentation. The proposed algorithm is shown to be robust to local noise and occlusion, because of its global nature. Experiments are performed on synthetic and real video sequences to demonstrate the capabilities of our approach.

We study the Stokes-Einstein (SE) and the Stokes-Einstein-Debye (SED) relations, Dt=kBT/6pietaR and Dr=kBT/8pietaR3, where Dt and Dr are the translational and rotational diffusivity, respectively, T is the temperature, eta the viscosity, kB the Boltzmann constant, and R the "molecular" radius. Our results are based on molecular dynamics simulations of the extended simple point charge model of water. We find that both the SE and SED relations break down at low temperature. To explore the relationship between these breakdowns and dynamical heterogeneities (DHs), we also calculate the SE and SED relations for subsets of the 7% "fastest" and 7% "slowest" molecules. We find that the SE and SED relations break down in both subsets, and that the breakdowns occur on all scales of mobility. Thus these breakdowns appear to be generalized phenomena, in contrast with a view where only the most mobile molecules are the origin of the breakdown of the SE and SED relations, embedded in an inactive background where these relations hold. At low temperature, the SE and SED relations in both subsets of molecules are replaced with "fractional" SE and SED relations, Dt approximately (tau/T)-xit and Dr approximately (tau/T)-xir, where xit approximately 0.84(<1) and xir approximately 0.75(<1). We also find that there is a decoupling between rotational and translational motion, and that this decoupling occurs in both the fastest and slowest subsets of molecules. Further, we find that, the decoupling increases upon cooling, but that the probability of a molecule being classified as both translationally and rotationally fastest also increases. To study the effect of time scale for SE and SED breakdown and decoupling, we introduce a time-dependent version of the SE and SED relations, and a time-dependent function that measures the extent of decoupling. Our results suggest that both the decoupling and SE and SED breakdowns originate at a time scale corresponding to the end of the cage regime, when diffusion starts. This is also the time scale when the DHs are more relevant. Our work also demonstrates that selecting DHs on the basis of translational or rotational motion more strongly biases the calculation of diffusion constants than other dynamical properties such as relaxation times.

In this work, it was studied the process of interaction between the Apocynin Dimer (DiApocynin -DiApo) and , or Cyclodextrin (CD). All processes were described considering the translational and rotational movements. The translational movement was considered along the z-axis followed by simultaneous rotational (circular) movements (from 0 to 360 o in intervals of 1.0 o ) of the Apocynin Dimer around its center of mass. It were generated molecular stru tures i these pro esses a d the al ulatio s o er i g the o for atio al a al sis of , and -CD DiApo were carried out using the PM3 semiempirical methodology. To the most sta le ole ular stru tures to , , -CD, a ordi g to statisti al ther od a i a al sis, were obtained the interaction energies of -5,251; -63,012 e -65,637 kJ.mol -at ONIOM2(B3LYP/6-31G(d):PM3) level of theory, respectively.

The expediency of the movement equations compiling of a vibro-insulated&#13;\nhousing of a gyroscopic system of classical type in a coordinate system, the start of&#13;\nwhich coincides with the center of mass of the entire device, is studied in this&#13;\npaper. The vibration protection system is believed to be formed by the elastic&#13;\nelements of the passive type.&#13;\nThe gyroscopic system consists of a sensitive element - a three-step gyroscope,&#13;\nwhich is located on a platform with a triaxial gimbal.&#13;\nThe general (basic) dynamics theorems are used to compile the movement&#13;\nequations.&#13;\nThe movement equation of each element of a gyroscopic system is written in a&#13;\nmoving coordinate system connected with its axis of suspension.&#13;\nThe movement equations of a vibration insulated device case are written in a&#13;\ncoordinate system that is tightly connected to it, the starting point of which&#13;\ncoincides with the point corresponding to the position of the center of mass of the&#13;\ngyroscopic system in the absence of mechanical perturbances.&#13;\nThe suspension centers of the platform frames are considered not to coincide&#13;\nwith the specified point. In turn, it is also assumed that the platform centers of&#13;\nmass and the outer frame do not coincide with their axises of suspension.&#13;\nThe system of equations of the rotational motion of a gyroscopic system is&#13;\nobtained by the method of Ishlinsky O. Yu., which excludes the unknown&#13;\ncomponents of the moments of interaction reactions between the gyro device&#13;\nelements.&#13;\nThe obtained scalar equations of the case rotational motion include components&#13;\nthat are projections of the moments of the housing inertia forces and the device&#13;\nelements caused by the absolute acceleration of the center of mass of the&#13;\ngyroscopic system together with the case. Since the gyroscopic system has moving&#13;\nelements, the resultant of these inertia forces is not applied at the center of mass of&#13;\nthe gyroscopic device and the case, but at a point whose position can be&#13;\ndetermined by the coefficients of the translational motion acceleration in the&#13;\nexpressions of these inertia forces moments equating them to zero. The last&#13;\nequalities allow us to find the position of the point at which the center of rigidity of&#13;\nthe vibration protection system should be located. This enables to avoid the&#13;\nappearance of interrelated angular and translational oscillations of the case caused&#13;\nby the potential forces distribution.&#13;\nThe translational motion equations of the gyroscopic system instrument are&#13;\nobtained by the theorem of the main vector change of the motion quantities&#13;\napplied to each element of the gyroscopic system with the subsequent exclusion of&#13;\nthe interaction forces between these elements. Angular velocities and angular&#13;\naccelerations of the device elements, which are included in the expressions of&#13;\nlinear accelerations, are proposed to be expressed through angular velocity and&#13;\nangular acceleration of the case. This allows to distinguish terms that determine&#13;\nthe impact of the angular movement of the suspension elements on the&#13;\ntranslational motion of the device case.&#13;\nThus, the refinement of the motion equations compiling method of the passive&#13;\nvibration protection system of the gyroscopic system is given in the paper. These&#13;\nequations are proposed to be written in the coordinate system axes connected with&#13;\nthe center of mass of the gyroscopic system together and the vibration insulated&#13;\ncase. The obtained equations allow to determine the requirements for rational&#13;\ninstallation of the vibration protection system, to evaluate the influence of the&#13;\ngyroscopic system on the angular and translational motion of the vibration&#13;\ninsulated case of the gyroscopic instrument.