Center Of Motion Research Articles

Rotating quantum Gaussian packets

We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the ‘external’ momentum related to the motion of the packet center and the ‘internal’ momentum due to quantum fluctuations. The packets minimizing the mean energy of an isotropic oscillator with the fixed mean angular momentum are found. They exist for ‘co-rotating’ external and internal motions, and they have nonzero correlation coefficients between coordinates and momenta, together with some (moderate) amount of quadrature squeezing. Variances of angular momentum and energy are calculated, too. Differences in the behavior of ‘co-rotating’ and ‘anti-rotating’ packets are shown. The time evolution of rotating Gaussian packets is analyzed, including the cases of a charge in a homogeneous magnetic field and a free particle. In the latter case, the effect of initial shrinking of packets with big enough coordinate-momentum correlation coefficients (followed by the well known expansion) is discovered. This happens due to a competition of ‘focusing’ and ‘de-focusing’ in the orthogonal directions.

Moving Object Acceleration/Deceleration Detection using Motion of Center of Gravity

Moving Object Acceleration/Deceleration Detection using Motion of Center of Gravity

On the motion of lumped‐mass and distributed‐mass self‐propelling systems in a linear resistive environment

The motion of self‐propelling limbless locomotion systems in a linear viscous environment is considered. The resistance (friction) force acting on an element of the systems is assumed to be proportional to the velocity of this element relative to the environment, the coefficient of proportionality (coefficient of friction) being constant. Two models of interaction of the locomotor with the environment are distinguished. In the first model, the coefficient of friction is constant for a mass element, whereas in the second model, this coefficient is constant for a length element. It is shown that progressive locomotion is impossible for the first model and is possible for the second model. This is explained by the fact that in the second model, the coefficient of friction for a mass element is in fact controlled by changing the length of this element due to deformation of the locomotor's body. The first model applies for lumped mass systems, while the second model is adequate for distributed mass limbless locomotors, like worms. For both models, the equations of motion of the system's center of mass are derived and analyzed.

Energetic Ion Acceleration by Small-scale Solar Wind Flux Ropes

We consider different limits of our recently developed kinetic transport theory to investigate the potential of supersonic solar wind regions containing several small-scale flux ropes to explain the acceleration of suprathermal ions to power-law spectra as observations show. Particle acceleration is modeled in response to flux-rope activity involving contraction, merging (reconnection), and collisions in the limit where the particle gyoradius is smaller than the characteristic flux-rope scale length. The emphasis is mainly on the statistical variance in the electric fields induced by flux-rope dynamics rather than on the mean electric field induced by multiple flux ropes whose acceleration effects are discussed elsewhere. Our steady-state analytical solutions suggest that ion drift acceleration by flux ropes, irrespective of whether displaying incompressible or compressible behavior, can yield power laws asymptotically at higher energies whereas an exponential spectral rollover results asymptotically when field-aligned guiding center motion acceleration occur by reconnection electric fields from merging flux ropes. This implies that at sufficiently high particle energies, drift acceleration might dominate. We also expect compressive flux ropes to yield harder power-law spectra than incompressible flux ropes.

Estimating forces in mixed eccentricities motion from purely dynamic eccentric rotor centre motion in a hydropower generator and their validation against EM simulations

Electromagnetic analysis of hydropower generators is common practice but there is little emphasis on studying the effect of rotor whirling in the analysis. This paper demonstrates the use of the unbalanced magnetic pull (UMP) curves based on purely dynamic eccentricity motion for a wide range of whirling frequencies in the prediction of the steady state UMP in the case of mixed eccentricities motion. The latter motion type is more realistic in practice. Actual electromagnetic (EM) simulations are also carried out for these mixed eccentricities motion cases in order to verify the proposed method. Good agreement between the UMP from the actual EM simulations and the UMP predictions are made when low eccentricities exist. The proposed method is thus very useful since firstly, very few EM software packages can handle mixed eccentricities motion and secondly, since actual EM simulations of intricate rotor centre motion are time-consuming, the proposed method is a big time saver. A modified feature selective validation (FSV) method, the FSV-UPC, is also applied to assess the similarities and the differences in the force computations.

Velocity of the mass center motion and duration evolution of pulses of a small number of oscillations in dispersive optical media

Analytical expressions for velocities of the center of mass and dispersive spreading of optical pulses with a small number of electromagnetic field oscillations in dielectric media have been obtained. For some typical time profiles of input pulses, these expressions are reduced to elementary functions of dispersion characteristics of the medium, central frequency of the pulse, and initial number of oscillations in it. It is shown that the duration of a terahertz pulse of one full-wave oscillation of the field can increase by a factor of \(\sqrt 2 \) when propagating in a dielectric to distances of only three central radiation wavelengths. For pulses of two full-wave oscillations of the field of the near-IR spectral range, the frequency of the zero group dispersion in a dielectric can shift by more than 200 nm.

Динамика параметров психофизиологических функций человека в условиях трансширотных перемещений

Adaptation is a fundamental property of organisms, which purpose is to keep quasi-attractors parameters within certain limits providing non equilibrium open systems in quasiattractor state. Parameter mismatch of functional systems, desynchronization of circadian rhythms, stability reduction of regulatory mechanisms in the conditions of the North are caused with extreme envi-ronmental parameters, chaotic oscillations of temperature and barometric modes, or socio-economic (information) changes. However, we can get the greatest expectations in this field by monitoring child population and older adults, as these are the most dangerous age groups in terms of sensitivity to ecological factors of Ugra. It is obvious that frequent vibrational motions of the state vector of the human organism do not allow it entering the stable quasi-attractor. For instance, long-term re-gimes of monotonous work, significant physical load or mental stress with short rest periods do not allow keeping the state vector of the human organism in quasi-attractors and accelerate the motion of quasi-attractor centers in the field of the mortal oscillatory rate.

Стохастическая и хаотическая оценка динамики параметров сердечно-сосудистой системы человека при трансширотных перемещениях.

Using the methods of statistical analysis and methods of multidimensional phase spaces (analysis and calculation of the volume of quasi-attractors matrices mezhattraktornyh distances) studied the behavior of the state vector of the body girls (for example, the behavior of the parameters of the cardiovascular system) with transshirotnyh movements. The differences in the assessment of the dynamic behavior of the parameters of the cardio-vascular system, namely the decrease in quasi-attractors indicates good revitalizing effect two-week stay in a boarding house young children oilman. Analysis matrices mezhattraktonyh distances showed that the motion of chaotic and stochastic centers at latitude movements somewhat different girls: mezhattraktornye distance when driving chaotic center upon arrival to rest down, after a two-week vacation, it becomes even more, to return to the city of Surgut is similar to the results for the arrival at rest, indicating the lack of formation of the girls adaptive mechanisms, as well as a significant tension of regulatory processes and the degree of mismatch of functional systems at transshirotnyh movements.

A study on dynamics of flexible multi-link mechanism including joints with clearance and lubrication for ultra-precision presses

It is essential to establish a dynamic model of flexible multi-link mechanism with clearance and lubrication for ultra-precision presses to analyze its dynamic response. Traditional dynamic models of mechanical system rarely consider the effect of flexibility, revolute and spherical clearance joints, and lubrication together, which causes lower precision analysis. In order to study the dynamic characteristics of multi-link mechanism more accurately, a novel dynamic model of flexible multi-link mechanism with clearance and lubrication for ultra-precision presses is established in the present work, which considers the effect of revolute and spherical clearance joints, lubrication, and flexibility of crank shaft and linkage. It is demonstrated that the dynamic responses of flexible multi-link mechanism with lubricated clearance joint model agree better with experimental data than those with dry clearance model and the validity of the proposed model is verified. The simulation results also show that the existence of lubrication reduces the dynamic responses of flexible multi-link mechanism with revolute and spherical clearance in a significant manner and act as a suspension for multi-link mechanism. The motion of the crank shaft center and ball center of spherical joint was mainly characterized by two phases: free flight and impact motion. Furthermore, the influences of the clearance size and input speed of crank shaft as well as blanking force on the dynamic responses of the multi-link mechanism were also investigated.

Study of Time-Resolved Vortex Structure of In-Cylinder Engine Flow Fields Using Proper Orthogonal Decomposition Technique

The structure of in-cylinder flow field makes significant impacts on the processes of fuel injection, air–fuel interactions, and flame development in internal combustion engines. In this study, the implementation of time-resolved particle image velocimetry (PIV) in an optical engine is presented. Flow field PIV images at different crank angles have been taken using a high-speed double-pulsed laser and a high-speed camera with seeding particles mixed with the intake air. This study is focused on measuring the flow fields on the swirl plane at 30 mm below the injector tip under various intake air swirl ratios. A simple algorithm is developed to identify the vortex structure and to track the location and motion of vortex center at different crank angles. Proper orthogonal decomposition (POD) has been used to extract the ensemble and variation information of the vortex structure. Experimental results reveal that strong cycle-to-cycle variations exist in almost all test conditions. The vortex center is difficult to identify since multiple, but small scale, vortices exist during the early stage of the intake stroke. However, during the compression stroke when only one vortex center exists in most cycles, the motion of vortex center is found to be quite similar at different intake swirl ratios and engine speeds. This is due to the dominant driving force exerted by the piston’s upward motion on the in-cylinder air.

A simple device for studying the relativity of motion

The fundamentals of classical mechanics are the foundation of more complicated and ingenious physical theories. Therefore, an educational experiment revealing to students the physical nature of mechanical phenomena is important. The effectiveness of this experiment manifoldly increases if students not only perform it by themselves, but also make the necessary appliances with their own hands. Such devices should be modern in order to elicit the students’ interest, and very simple so that creating them does not require much time and effort. This paper proposes a device that can be used in the experimental study of the relativity of mechanical motion and in the investigation of the motion of the solid mass centre in the Earth’s gravitational field. The device is a soft disc into which a power supply, a switch, a pulse generator and two coloured light emitting diodes are fixed, so that the mass centre of the device does not coincide with the geometrical centre of the disc. One of the diodes is placed in the mass centre, and the other is located at the edge of the disc. Several interesting examples are considered as the body mass centre moves along a parabola, a cycloid and a straight line.

Development of the SAIT single-port surgical access robot--slave arm based on RCM mechanism.

An innovative single-port surgical robot has recently been developed by the Samsung Advanced Institute of Technology (SAIT). The robot can reach various surgical sites inside the abdominal cavity from a single incision on the body. It has two 7-DOF surgical tools, a 3-DOF endoscope, a flexible hyper-redundant 6-DOF guide tube, and a 6-DOF manipulator. This paper primarily focuses on the manipulator, called a slave arm, which is capable of setting the location of a Remote Center Motion (RCM) point. Because the surgical tools can explore the abdominal area through a small incision point when the RCM point is aligned with the incision area, the RCM mechanism is an integral part of the manipulator for single-port surgery. The mechanical feature, operational principle, control method, and the system architecture of the slave arm are introduced in this paper. In addition, manipulation experiments conducted validate its efficacy.

Optimization and preoperative adjustment design of remote center motion mechanism for minimally invasive surgical robot

Abstract In this paper, a new remote center motion (RCM) mechanism called triangle is proposed; this mechanism is simple and with high stiffness. A complete kinematic analysis and optimization algorithm implying AHP which is a combination of quantitative and qualitative analysis method incorporating the requirements for minimally invasive surgery (MIS) are performed to find the optimal link lengths of the manipulator. The results show that for the serial triangle two-link manipulator used to guide the surgical tool, the optimization link angles are 74° and 51°. Prior preoperative adjustment is usually realized by electromagnetic clutch. However, the disadvantage of this method is that the joint is complex, big, and heavy because of gravity balance mechanism. A new preoperative adjustment method realized by resistance compensation is proposed without electromagnetic clutch; the joint is simpler and lighter than the conventional joint.

Interaction of a magnet and a point charge: Unrecognized internal electromagnetic momentum

Whereas nonrelativistic mechanics always connects the total momentum of a system to the motion of the center of mass, relativistic systems, such as interacting electromagnetic charges, can have internal linear momentum in the absence of motion of the system's center of energy. This internal linear momentum of a system is related to the controversial concept of “hidden momentum.” We suggest that the term “hidden momentum” be abandoned. Here, we use the relativistic conservation law for the center of energy to give an unambiguous definition of the “internal momentum of a system,” and then we exhibit this internal momentum for the system of a magnet (modeled as a circular ring of moving charges) and a distant static point charge. The calculations provide clear illustrations of this system for three cases: (a) the moving charges of the magnet are assumed to continue in their unperturbed motion; (b) the moving charges of the magnet are free to accelerate but have no mutual interactions; and (c) the moving charges of the magnet are free to accelerate and also interact with each other. When the current-carrying charges of the magnet are allowed to interact, the magnet itself will contain internal electromagnetic linear momentum, something that has not been described clearly in the research and teaching literature.

Markerless tracking of small lung tumors for stereotactic radiotherapy.

(1) To validate retrospective markerless tracking software for small lung tumors by comparing tracked motion in 4-dimensional planning computed tomography (4DCT) derived kV projection images and known tumor motion in the same 4DCT. (2) To evaluate variability of tumor motion using kV projection images from cone-beam computed tomography (CBCT) scans acquired on different days. Nonclinical tumor tracking software (TTS) used a normalized cross correlation algorithm to track the tumor on enhanced kV projection images (e.g., from a CBCT scan). The reference dataset consisted of digitally reconstructed radiographs (DRRs) from one phase of a planning 4DCT. TTS matches two in-plane coordinates and obtains the out-of-plane coordinate by triangulating with match results from other projections. (1) To validate TTS, tracking results were compared with known 4DCT tumor motion for two patients (A and B). Projection images (1 image/1°) were digitally reconstructed for each 4DCT phase. From these, kV projection series were composed simulating full breathing cycles every 20° of gantry rotation [breathing period = 20°/(6°/s) = 3.33 s]. Reference templates were 360 "tumor enhanced" DRRs from the 4DCT expiration phase. TTS-derived tumor motion was compared to known tumor motion on 4DCT. (2) For five patients, TTS-assessed motion during clinical CBCT acquisition was compared with motion on the planning 4DCT, and the motion component in the Y (cranio-caudal)-direction was compared with the motion of an external marker box (RPM, real-time position management). (1) Validation results: TTS for case A (tumor 6.2 cm(3), 32 mm axial diameter) over 360° showed mean motion X (medial-lateral) = 3.4, Y = 11.5, and Z (ventral-dorsal) = 4.9 mm (1 SD < 1.0 mm). Corresponding 4DCT motion was X = 3.1, Y = 11.3, and Z = 5.1 mm. Correlation coefficients between TTS tumor motion and displacement of the tumor's center of mass (CoM) on 4DCT were 0.64, 0.96, and 0.82 (X, Y, and Z, respectively). For case B (4.1 cm(3), 20 mm diameter), due to temporarily decreased tumor visibility preventing TTS from resolving the tumor, robust tracking data were only available between angles 300°-40° and 120°-220°. Mean motion according to TTS was X = 2.0, Y = 7.7, and Z = 8.2 mm (1 SD < 0.9 mm). Tumor motion on 4DCT was X = 1.8, Y = 7.6, and Z = 9.5 mm and correlation coefficients between TTS motion and CoM displacement were 0.59, 0.95, and 0.93 (X, Y, and Z, respectively). (2) CLINICAL RESULTS: TTS revealed a mean intrafraction variation in tumor motion in Y-direction of >2.0 mm (1 SD) in four of five patients. In addition, clinical tumor motion amplitude differed from that seen on planning 4DCT. Internal and external structures that create abrupt density change (e.g., table-top edge, interface between lung/mediastinum and lung/heart) were observed to prevent 360° tracking of the tumor. Correlation coefficients between TTS motion in the Y-direction and the RPM signal (22 observations) ranged from 0.78 to 0.96. In 2D, 241 TTS matches at end-inspiration and end-expiration were visually validated: mean difference was 0.8 mm (SD = 0.7) for both. TTS can track small lung tumors if these are visible in kV projections. A 4DCT dataset can be used to validate kV tracking of moving targets. TTS and 4DCT displacement agreed to within 2 mm. TTS and RPM motion were closely associated but tumor motion during CBCT can vary from the planning 4DCT.

Modeling and analysis of dynamics for spacecraft relative motion actuated by inter-satellite non-contacting force

With the recent flurry of research on spacecraft relative motion actuated by inter-satellite non-contacting force, i.e., electrostatic force, electromagnetic force and magnetic flux-pinned force, the need has become apparent for dynamic modeling and dynamics analysis that capture the characteristics of this generic force. Based on the basic derivation of electrostatic force model and some theorems, the actuations of electrostatic force, electromagnetic force/torque and magnetic flux-pinned force/torque are unified and the corresponding mathematic models are derived. And then, with a general notation of this inter-satellite non-contacting force, the dynamic models are developed with respect to several assumptions of circular orbit, elliptical orbit and general Keplerian orbit pertaining to the motion of center of mass of the spacecraft cluster. A detailed dynamics analysis based on these derived models are carried out, including constraints of the relative motion dynamics, the special characteristics of applications to the near-Earth relative orbit motion and the deep space relative motion, and then a case with co-rotating pair of satellites subject to the previously mentioned inter-satellite non-contacting forces was simulated to validate the dynamic modeling and dynamics analysis. At last, some useful conclusions follow.

Biosystem kinematics as evolution: Stationary modes and movement speed of complex systems: Complexity

It is proposed to construct the kinematics of complex systems (systems of the third type) based on simulation of the motion of the state vector of the system x(t) in the phase space of states. A new concept of stationary modes of these systems, which is different from the analog in mechanics (when dx/dt = 0) and statistical interpretation (when the distribution function f(x) does not change significantly), is introduced. For systems of the third type, dx/dt ≠ 0 is always met and f(x) for all consecutive samples (e.g., cardiointervals) varies continuously. A unit for calculation of the motion of centers of quasi-attractors (QA, regions of phase space, where x(t) changes continuously) is presented. The concepts of velocity and acceleration of evolution are introduced. The concepts of uncertainty of the first and second kinds are given. Examples of rectilinear and curvilinear motion of x(t) in the phase space (from gerontology for groups of women of different ages) are given.

Drifts of electron orbits induced by toroidal electric field in tokamaks

The drifts of electron orbits induced by the toroidal electric field in tokamaks are analyzed. Based on the relativistic Hamiltonian equations for guiding centre motion, the formula for the drift velocity vdr is derived. It describes the outward drift of passing particles as well as the inward drift (the Ware pinch) of trapped particles. Unlike the approximate formula for vdr given in Guan et al. [Phys. Plasmas 17, 092502 (2010)] for circular electron orbits, it describes qualitatively new features of the outward drift of electron orbits. Particularly, the new formula describes the evolution of the orbit's shape, the formation of X-point and the associated separatrix. It is shown that the outward drift velocity is proportional to the inverse aspect ratio of tokamaks.

Nonlinear dynamics of a rotating triangular tethered satellite formation near libration points

The nonlinear coupled dynamics of a rotating triangular tethered satellite formation near libration points is presented. Based on Hill's approximation, the dynamical formulation for a rotating triangular tethered system near libration points is developed. The formulation comprises a set of strong nonlinear coupled equations. Numerical simulations using the full nonlinear and time-varying motion equations are performed for the station-keeping stages. The dynamic characteristics of the triangular tethered formation are analyzed. The numerical results demonstrate that the rotation rate has a significant impact on the stability of the system, whereas the orbital amplitude has a moderate impact on the stability of the system. Tether length has little effect on the motion of the system's center of mass. It can be served as a basis to solve the problem of rotating triangular tethered systems in any arbitrary plane.

Dynamics and morphology of single ellipsoidal bubbles in liquids

A data postprocessing method for an imaging technique based on shadowgraphy is presented in this paper. It enables a precise analysis of the dynamics of a bubble rising in a liquid. The morphology of the bubble is also precisely analyzed by determining an appropriate threshold for the binarization of the images. Experiments with single ellipsoidal bubbles rising in various water–glycerol mixtures, with an oscillatory trajectory and without interface wobbling, are analyzed. It is rigorously shown that the minor axis and the mass center velocity vector of a bubble are aligned in the cases of a zigzag and a helical motion of the bubble. The interface curvature radii at the front and at the rear of a bubble are determined and, in the case of a zigzag motion of the bubble, a correlation to calculate their ratio is proposed. In the vertical motion of the mass center of a bubble, a pulsation at twice the frequency of its horizontal motion is identified in the case of a zigzag motion of the bubble. In the case of a helical motion of a bubble, such a pulsation cannot be identified in the vertical motion of the mass center of the bubble.