Center Of Motion Research Articles

Combining forces and kinematics for calculating consistent centre of mass trajectories

The motion of centre of mass (CoM) is a fundamental object of investigation in biomechanical analysis. In principle, the CoM motion can either be calculated from force data (dynamic method) or motion capture data (kinematic method). In both approaches, the accuracy of the calculated trajectories depends on the quality of the original signals. Interestingly, the inaccuracies in each method are related to different parts of the Fourier spectrum. Here, we present a new approach to compute CoM motion based on the reliable frequency range of force and kinematic measurements. As a result we obtain physically consistent CoM and force signals, i.e. the second derivative of the CoM trajectory equals the force. The algorithm is verified on simulation data and applied to selected experimental data. We show that the new algorithm can eliminate typical inaccuracies inherent in kinematic and force signals. Also, we discuss the biological and technical origins of these findings.

DAMPED VIBRATIONS PROBLEM OF BEAMS FIXED ON THE ROTATIONAL DISK

The problem considered in this paper is one of damped vibrations of the beam in transportation. The dynamical analysis of systems in motion is a very well-known issue, but many detailed cases have not been published yet. The considered case is applied with the double-sided fixed beams placed on a rotational disk. The disk treated as a rigid one is rotated with a constant angular velocity in the stationary reference frame. An application of vibrations of the beam is transformed from a local to global reference frame, damping forces and forces arising from the rotational motion of a local reference center are also taken into consideration. The beam is assumed as a homogenous one with symmetric cross-sections. This work is the dynamical analysis of such a type of vibrations, which is a mathematical one based on considering transient response and dynamical flexibility of this type of systems.

Intermediate-mass black holes in globular clusters

The mass of central bodies in a number of Milky-Way globular clusters is estimated based on the stellar radial-velocity dispersion data. It is assumed that stars located close to the center of the cluster (i.e., to the black hole) rotate about it, have masses on the order of the solar mass, and that the mass of the gravitating center is greater by a factor of 1000. The radial velocities of stars in the vicinity of cluster centers are analyzed for two hypothetical extreme cases: (1) ordered orbital motion of stars about the gravitating center and (2) chaotic orbital motions. The masses inferred for most of the clusters (102–104M⊙) correspond to intermediate-mass black holes. Another important result of this study consists in the determination of the quantity l, the characteristic scale length of the additional spatial dimension. Given the age and mass of the globular cluster NGC 6397 we estimate l to be between 0.02 and 0.14 mm.

Charged particle motion in electromagnetic fields varying moderately rapidly in space

Electromagnetic fields are considered which vary on the space scale of the geometric mean of the Larmor radius and the much larger scale length of variation of the magnetic field lines. It is first shown that the magnetic moment is an adiabatic invariant, even though the usual arguments for its existence fail. The motion of the guiding center is then examined. For perpendicular drifts in magnitude comparable with the particle speed, the subsequent motion is dominated by electrostatic effects. The motion of particles along the field lines occurs on a much slower time scale than the perpendicular drift time scale. When the guiding center motion is approximately periodic in time, a second adiabatic invariant exists, the magnetic flux enclosed by the almost periodic orbit. When the perpendicular drift is small compared with the particle speed, the parallel motion and the perpendicular drift occur on the same, slow timescale.

Biomechanics of octopedal locomotion: kinematic and kinetic analysis of the spiderGrammostola mollicoma

Despite the abundance of octapodal species and their evolutionary importance in originating terrestrial locomotion, the locomotion mechanics of spiders has received little attention so far. In this investigation we use inverse dynamics to study the locomotor performance of Grammostola mollicoma (18 g). Through 3-D kinematic measurements, the trajectory of the eight limbs and cephalothorax or abdomen allowed us to estimate the motion of the body centre of mass (COM) at different speeds. Classic mechanics of locomotion and multivariate analysis of several variables such as stride length and frequency, duty factor, mechanical external work and energy recovery, helped to identify two main gaits, a slow (speed <11 cm s(-1)) one and a fast one characterised by distinctive 3-D trajectories of COM. The total mechanical work (external + internal) calculated in the present study and metabolic data from the literature allowed us to estimate the locomotion efficiency of this species, which was less than 4%. Gait pattern due to alternating limb support, which generates asymmetrical COM trajectories and a small but consistent energy transfer between potential and kinetic energies of COM, is discussed both in terms of coordination indices and by referring to the octopod as formed by two quadrupeds in series. Analogies and differences of the newly obtained parameters with the allometric data and predictions are also illustrated.

Dynamics of breakup of multiple vortices in Gross-Pitaevskii equations of superfluids

In this paper we study the Gross-Pitaevskii equation of the theory of superfluidity, i.e., the nonlinear Schrödinger equation of the Ginzburg-Landau type. We investigate the dynamics of the breakup of the double vortex. More specifically, we prove instability of the double vortex, compute the complex eigenvalue responsible for this instability, and derive the dynamical equation of motion of (centers of) single vortices resulting from splitting of the double vortex. We expect that our analysis can be extended to vortices of higher degree and to magnetic and Chern-Simmons vortices.

A statistical physics perspective on the evolution of ion distributions across low Mach number quasi-perpendicular collisionless shocks

[1] The heating of directly transmitted ions at low Mach number, perpendicular and quasi-perpendicular shocks has been the subject of previous statistical physics studies. In this paper, we use a Hamiltonian formulation of the ion kinetics for a quasi-perpendicular shock model to derive the general solution to Liouville's equation as a function of six invariants, finding forms of these invariants in terms of the upstream parameters. The ion distribution is expressed as a function of one of these invariants, subject to a Maxwellian upstream boundary condition, and the evolution of the distribution through and downstream of the shock is studied. The momentum-space volume within surfaces of constant probability (related to the temperature) is shown to be inversely proportional to an average value of the canonical momentum associated with motion in the direction normal to the shock plane, generalizing a previous result to three-dimensional phase space. We also study the evolution of the distribution properties numerically, in particular noting that the “twisting” of these surfaces in phase space is the result of the unequal guiding center motion of different parts of the distribution (which is not the case for a fully perpendicular shock). This property provides insight into the damping of oscillations in the mean momentum and the temperature for a quasi-perpendicular model (as the distribution is spread about the central value through gyration) and the observed T⊥ > T∥ anisotropy.

The role of drift orbit bifurcations in energization and loss of electrons in the outer radiation belt

[1] Radiation levels in Earth's outer electron belt (L ≳ 2.5) vary by orders of magnitude on the time scales ranging from minutes to days. Multiple acceleration and loss processes operate across the belt and compete in defining its global variability. One such process is the drift orbit bifurcation effect. Caused by coupling of the drift and bounce motions, it breaks the second adiabatic invariant of radiation belt electrons producing their transport in radius and pitch angle. In this paper we investigate implications of drift orbit bifurcations to the global state and variability of the outer electron belt. For this purpose we use three-dimensional test particle simulations of electron guiding center motion in a realistic magnetic field model. We show that even at most quiet solar wind conditions bifurcations affect a broad range of the belt penetrating inside the geosynchronous orbit. This has an important practical implication for the analysis of experimental particle data: since the third adiabatic invariant is undefined for bifurcating orbit, the electron phase space density cannot be expressed in terms of three adiabatic invariants. We show that long-term transport of electrons due to drift orbit bifurcations is a complex combination of large ballistic jumps and small-amplitude diffusion in the second invariant and radial location. To model long-term transport, we derive an empirical map of the second invariant and radial jumps at bifurcations. The map can also be implemented by other radiation belt models, which cannot directly account for the physics of drift orbit bifurcations. Drift orbit bifurcations can produce electron losses through the magnetopause escape and through pitch angle scattering into the atmospheric loss cone. Most electrons, however, can stay quasi-trapped in the bifurcation regions for very long time periods. The pitch angle and radial transport due to drift orbit bifurcations lead to their meandering back and forth across the region producing mixing and recirculation of particle populations with different initial conditions. We show that this recirculation can greatly amplify electron energization by radial diffusion. Compared to the diffusion alone, the combined action of radial diffusion and drift orbit bifurcations can double electron energization at each recirculation cycle. Our results suggest that drift orbit bifurcations can play an important role in the buildup of increased electron fluxes in the storm recovery phase.

Kinetic simulations of fast ions in stellarators

The steady-state distribution function of neutral beam injection (NBI) fast ions is calculated numerically for the LHD and TJ-II stellarators using the code ISDEP (Integrator of Stochastic Differential Equations for Plasmas). ISDEP is an orbit code that solves the guiding centre motion of fast ions using Cartesian coordinates in position space, allowing arbitrary magnetic configurations and the re-entering of particles in the plasma. It takes into account collisions of fast ions with thermal ions and electrons using the Boozer and Kuo-Petravic collision operator. The steady-state distribution function is computed with a time integral following Green's function formalism for a time-independent source. The rotation profiles of the fast ions are also estimated, thus computing their contribution to the total plasma current. In addition, energy slowing down time and escape distribution are studied in detail for both devices.

Nonequilibrium forces between atoms and dielectrics mediated by a quantum field

In this paper we give a first principles microphysics derivation of the nonequilibrium forces between an atom, treated as a three dimensional harmonic oscillator, and a bulk dielectric medium modeled as a continuous lattice of oscillators coupled to a reservoir. We assume no direct interaction between the atom and the medium but there exist mutual influences transmitted via a common electromagnetic field. By employing concepts and techniques of open quantum systems we introduce coarse-graining to the physical variables - the medium, the quantum field and the atom's internal degrees of freedom, in that order - to extract their averaged effects from the lowest tier progressively to the top tier. The first tier of coarse-graining provides the averaged effect of the medium upon the field, quantified by a complex permittivity (in the frequency domain) describing the response of the dielectric to the field in addition to its back action on the field through a stochastic forcing term. The last tier of coarse- graining over the atom's internal degrees of freedom results in an equation of motion for the atom's center of mass from which we can derive the force on the atom. Our nonequilibrium formulation provides a fully dynamical description of the atom's motion including back action effects from all other relevant variables concerned. In the long-time limit we recover the known results for the atom-dielectric force when the combined system is in equilibrium or in a nonequilibrium stationary state.

Experimental Determination of Horizontal Motion of Human Center of Gravity During Squatting

The excursion of the center of gravity (COG) line is often examined in terms of balance control, standing, walking or running locomotion, etc. Although these examinations are carried out on multiple human subjects, the obtained results are not bound to any “human-like” quantity such as the anatomically well-defined and widely accepted angle of flexion. This paper is meant to prove the following hypotheses: the horizontal excursion of the COG line changes its position during squatting in contrary with steady-state assumption and it can be derived as a single empirical function of flexion angle. A test setup was developed for the experiments, alongside with an experiment protocol and a special construction method to obtain the results. During the experiments, 16 healthy, male and female participants’ data were used as a basis for the dimensionless λfunctions. The results showed common characteristics between the subjects’ data, and suggested that the general relationship between the squatting and the excursion of COG can be described with linear, dimensionless functions. As a final goal of this study, the obtained dimensionless functions will be used in a mathematical model, which is being developed.

Assessment of Organ Motion in Postoperative Endometrial and Cervical Cancer Patients Treated With Intensity-Modulated Radiation Therapy

Intensity-modulated radiation therapy (IMRT) may be useful to reduce toxicity in gynecologic cancer patients requiring postoperative pelvic irradiation. This study was undertaken to quantify vaginal wall organ motion during the course of postoperative pelvic irradiation using pelvic IMRT. Twenty-two consecutive patients treated with postoperative pelvic IMRT on helical tomotherapy had fiducial markers placed at the vaginal apex prior to simulation then daily megavoltage computed tomography (CT) scans for positioning. The daily positions of the fiducials were registered and measured in reference to the initial CT scan to quantify the degree of vaginal wall organ motion during the entire course of therapy. The total motion of the fiducials center of mass (COM) was a median of 5.8 mm (range, 0.6-20.2 mm), and 95% of all COM positions fell within 15.7 mm of their original position. Directional margins of 3.1 mm along the right-left axis, 9.5 mm along the superoinferior axis, and of 12.1 mm along the anteroposterior axis encompassed the vaginal fiducials in 95% of treatments. Mean organ deformation for all patients was 3.9 mm, (range, 0-27.5 mm; standard deviation, 3.1 mm), with significant distortions of greater than 10 mm in 17% of secondary image sets. These data suggest a planning target volume margin of 16 mm will account for maximal organ motion in the majority of gynecologic patients undergoing postoperative pelvic IMRT, and it may be possible to incorporate directional motion into the planning target volume margin.

A multiparameter family of phase portraits in the dynamics of a rigid body interacting with a medium

The problem of plane-parallel motion of a uniform symmetric rigid body interacting with a medium only through a flat region of its outer surface is studied. The force field is constructed on the basis of information on the properties of jet flow under quasistationarity conditions. The motion of the medium is not studied. The problem of rigid body dynamics is considered for the case when the characteristic time of motion of the body relative to its center of mass is comparable with the characteristic time of motion of this mass center.

TIME-DEPENDENT PERPENDICULAR TRANSPORT OF FAST CHARGED PARTICLES IN A TURBULENT MAGNETIC FIELD

We present an analytic derivation of the temporal dependence of the perpendicular transport coefficient of charged particles in magnetostatic turbulence, for times smaller than the time needed for charged particles to travel the turbulence correlation length. This time window is left unexplored in most transport models. In our analysis all magnetic scales are taken to be much larger than the particle gyroradius, so that perpendicular transport is assumed to be dominated by the guiding center motion. Particle drift from the local magnetic field lines (MFLs) and magnetic field line random walk are evaluated separately for slab and three-dimensional (3D) isotropic turbulence. Contributions of wavelength scales shorter and longer than the turbulence coherence length are compared. In contrast to the slab case, particles in 3D isotropic turbulence unexpectedly diffuse from local MFLs; this result questions the common assumption that particle magnetization is independent of turbulence geometry. Extensions of this model will allow for a study of solar wind anisotropies.

Small Tooth Number Difference Planetary Gear Drive with a Crank and Oscillating Block Inputting Mechanism

A new mechanism construction for small tooth number difference planetary gear drive is developed in which the planet wheel is guided by a planar crank and oscillating block mechanism. The sizes of linkage are design dexterously to get an approximate circumference linkage curve so that the engaging condition of internal gear pair can be satisfied. The trajectory of the inner gear center motion is analyzed and its error comparing with a standard circle is calculated to avoid movement interference. The movement of inner gear is study particularly to deduced formula of instantaneous transmission ratio. Despite observable fluctuation of output speed, this new type of gear transmission mechanism still has potential application value in situation with large ratio and low input speed. A hand drive winch prototype using the mechanism is also illustrated in this paper.

Analyzing pedestrian head injury to design pedestrian-friendly hoods

Head injuries are a major cause of fatalities in pedestrian-car accidents. The HIC (Head Injury Criterion) value, a measure of the fatality risk of a head injury, is calculated from the acceleration of the head’s center of gravity (henceforth, head center) resulting from a head impact. The pedestrian’s head does not impact the hood at a direction normal to the hood’s surface. The direction of motion of the head center may change extremely rapidly upon impact, and normal acceleration may also significantly contribute to the resultant acceleration of the head center. Therefore, pedestrian head protection studies should consider how normal acceleration contributes to the resultant acceleration of the head center. It is necessary to control the resultant acceleration of the head center to produce an optimal characteristic pulse. This study analyzes the composition and variations of the head’s acceleration in head-to-hood impacts, focusing on exactly how the normal and tangential components of the acceleration contribute to the resultant acceleration of the head center. This study also considers how structural design parameters affect each component of the resultant acceleration. Methods to control the resultant acceleration of the head center to produce an optimal characteristic pulse can be proposed based on the results of this study. The analytical models and the results of this study contribute to efforts to design vehicle hoods and pave the way for developing pedestrian protection technologies.

Rectified motion of a Bose-Einstein condensate in a horizontally vibrating shallow optical lattice

We consider a Bose-Einstein condensate, described by the Gross-Pitaevskii equation, in a horizontally vibrating shallow optical lattice. We study the dynamics of a bright soliton using the collective coordinate approximation. We show that depending on the parameters, amplitude, and frequency of the vibration of the lattice, the phase space of the equation of motion for the soliton center of mass shows multistability. In the frequency locked regions, in which the soliton has a nonzero average velocity determined by the external frequency, the motion is quasiperiodic, and between the locked regions the soliton moves chaotically.

Dielectric Properties and Electron Paramagnetic Resonance of Nanocrystalline Potassium Tantalate

Dielectric constant, losses, and Electron Paramagnetic Resonance (EPR) spectra of the nanocrystalline potassium tantalate were obtained and investigated. In the temperature dependence of the dielectric constant, a wide peak in the interval 20 < T < 40 K was observed. Maximum value of ϵ is 390. This dielectric peak did not shift to higher temperature as the measuring frequency was increased from 25 Hz to 1 MHz. Dielectric losses have several low-temperature frequency-dependant peaks. Obviously, these peaks reflect the reorientation motion of the dipole centers in the material. EPR spectra of nanocrystalline potassium tantalate consist of two types of signals—a ferromagnetic and a paramagnetic signal.

A46 パーキンソン病患者の立ち上がり動作解析に関する研究(傷害・障害II)

In this study, the model which can calculate the velocity at seat-off in success to assist the sit-to-stand movement for parkinson's disease patiants is proposed. The model expresses the motion of center of gravity by using a telescopic inverted pendulum model. In order to identify the relationship between the velocity at seat-off and floor reaction force, the experiment is carried out. Based on the experimental results, a floor reaction force was made. By obtaining the floor reaction force, the velocity at seat-off can be changed. We conclude that the model can express sit-to-stand movement in success and failure.

Lycra® arm splints improve movement fluency in children with cerebral palsy

AimsTo determine changes in upper limb movement substructures that denote fluency of movement in children with cerebral palsy (CP) following lycra® splint wear. Secondarily, to explore the efficacy of lycra® splints for those with spastic and dystonic hypertonia. DesignRandomised clinical trial whereby participants were randomised to parallel groups with waiting list control. MethodSixteen children (mean age 11.5 years SD=2.2) with hypertonic upper limb involvement (13 hemiplegia, 4 quadriplegia) were recruited. Children were randomly allocated either to a control group or to wear the lycra® splint for a period of three months. Three-dimensional (3D) upper limb kinematics was used to assess four functional tasks at baseline, on initial lycra® splint application, three months after lycra® splint wear, and immediately after splint removal. Movement substructures of the motion of the wrist joint center were analysed. ResultsA significant difference was observed between baseline and three months of lycra® splint wear in the movement substructures; movement time, percentage of time and distance in primary movement, jerk index, normalised jerk and percentage of jerk in primary and secondary movements. The magnitude of changes in normalised jerk and the percentage of jerk in the primary movement from baseline to three months was greatest in children with dystonic hypertonia. ConclusionsThe results indicate that lycra® arm splinting induced significant changes in movement substructures and motor performance in children with CP. This research demonstrates that fluency of movement can be quantified and is amenable to change with intervention.