new analytical free vibration solutions of orthotropic rectangular thin plates using generalized integral transformation abstract a first endeavor is made to obtain the analytical free vibration solutions of orthotropic rectangular thin plates utilizing the generalized integral transformation technique owing to the nature of the problem it is very hard to get the exact solution of the title problem by common inverse semi inverse method in solution procedure the vibrating beam function is selected as the integral core to form the generalized integral transformation pair then the high order partial differential equation under specific boundary conditions is converted to linear algebraic equations and the exact solution is achieved in a straightforward way one of the advantages of the proposed method is its simplicity and versatility and does not require pre determining the deflection function which makes the solving procedure more reasonable the method has wide applications range and can handle other elastic plate problems such as shear buckling buckling and bending the present results are validated by comparing with the existing analytical solutions which show satisfactory agreement

semiclassical asymptotics gauge fields and quantum chaos a gauge field is given by a connection on a principal bundle p m we consider the semiclassical behavior of a family of schrodinger operators associated with a gauge field in the limit as h 0 we relate the spectral theory of such operators to behavior of the hamiltonian flow on the natural phase space associated to a gauge field examining in particular situations where this flow exhibits chaotic behavior

dynamic response of clamped axially moving beams integral transform solution the generalized integral transform technique gitt is employed to obtain a hybrid analytical numerical solution for dynamic response of clamped axially moving beams the use of the gitt approach in the analysis of the transverse vibration equation leads to a coupled system of second order differential equations in the dimensionless temporal variable the resulting transformed ode system is then solved numerically with automatic global accuracy control by using the subroutine divpag from imsl library excellent convergence behavior is shown by comparing the vibration displacement of different points along the beam length numerical results are presented for different values of axial translation velocity and flexural stiffness a set of reference results for the transverse vibration displacement of axially moving beam is provided for future co validation purposes

stationary scattering in the semi classical limit for a schrodinger operator in a gauge field abstract we study the classical limit of the stationary scattering theory for a schrodinger operator in a compactly supported gauge field we show that under suitable hypotheses on the associated classical flow the scattering amplitude has a complete asymptotic expansion in the semi classical parameter and we determine the main term of this expansion

analytical study of the effects of soft tissue artefacts on functional techniques to define axes of rotation abstract the accurate location of the main axes of rotation aor is a crucial step in many applications of human movement analysis there are different formal methods to determine the direction and position of the aor whose performance varies across studies depending on the pose and the source of errors most methods are based on minimizing squared differences between observed and modelled marker positions or rigid motion parameters implicitly assuming independent and uncorrelated errors but the largest error usually results from soft tissue artefacts sta which do not have such statistical properties and are not effectively cancelled out by such methods however with adequate methods it is possible to assume that sta only account for a small fraction of the observed motion and to obtain explicit formulas through differential analysis that relate sta components to the resulting errors in aor parameters in this paper such formulas are derived for three different functional calibration techniques geometric fitting mean finite helical axis and sara to explain why each technique behaves differently from the others and to propose strategies to compensate for those errors these techniques were tested with published data from a sit to stand activity where the true axis was defined using bi planar fluoroscopy all the methods were able to estimate the direction of the aor with an error of less than 5 whereas there were errors in the location of the axis of 30 40 mm such location errors could be reduced to less than 17 mm by the methods based on equations that use rigid motion parameters mean finite helical axis sara when the translation component was calculated using the three markers nearest to the axis

on the use of orthogonal polynomials in the rayleigh ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates series composed of recently proposed orthogonal polynomial functions are used in the rayleigh ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates it is demonstrated that the approach yields excellent results not only for natural frequencies and buckling loads but also for the more sensitive mode shape bending moment and shear force distribution problem

small ħ asymptotics for quantum partition functions associated to particles in external yang mills potentials to a gauge field on a principalg bundlep m is associated a sequence of quantum mechanical hamiltonians as planck s constant 0 and a sequence of representations n ofg is taken this paper studies the associated quantum partition functions trace exp th n and produces a complete asymptotic expansion as 0 1 n of which the principal term proportional to the classical partition function is the familiar classical limit

estimation of the axis of a screw motion from noisy data a new method based on plucker lines the problems of estimating the motion and orientation parameters of a body segment from two n point set patterns are analyzed using the plucker coordinates of a line plucker lines the aim is to find algorithms less complex than those in conventional use and thus facilitating more accurate computation of the unknown parameters all conventional techniques use point transformation to calculate the screw axis in this paper we present a novel technique that directly estimates the axis of a screw motion as a plucker line the plucker line can be transformed via the dual number coordinate transformation matrix this method is compared with schwartz and rozumalski 2005 a new method for estimating joint parameters from motion data journal of biomechanics 38 107 116 in simulations of random measurement errors and systematic skin movements simulation results indicate that the methods based on plucker lines plucker line method are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements this investigation yielded practical results which can be used to locate the axis of a screw motion in a noisy environment developing the dual transformation matrix dtm from noisy data and determining the screw axis from a given dtm is done in a manner analogous to that for handling simple rotations a more robust approach to solve for the dual vector associated with dtm is also addressed by using the eigenvector and the singular value decomposition

a survey of formal methods for determining the centre of rotation of ball joints abstract the determination of an accurate centre of rotation cor from segment marker positions is of interest across a wide range of applications but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee for limb alignment purposes for the first time in this survey of formal methods we classify analyse and compare different methods geometric algebraic bias compensated algebraic and pratt sphere fit methods as well as the centre transformation technique the holzreiter approach the helical pivot technique the schwartz transformation techniques the minimal amplitude point method and the stoddart approach for the determination of spherical joint centres from marker position data in addition we propose a new method the symmetrical cor estimation or score in which the coordinates of the joint centre must only remain constant relative to each segment thus not requiring the assumption that one segment should remain at rest for each method 1000 cor estimations were analysed with the application of isotropic independent and identically distributed gaussian noise standard deviation 0 1 cm to each of the marker positions to all markers on the segment simultaneously and the two in combination for the test conditions used here most techniques were capable of determining the cor to within 0 3 cm as long as the spherical range of motion rom of the joint was 45 or more under the most stringent conditions tested however the score was capable of best determining the cor to within approximately 1 2 mm with a rom of 20 the correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement

new least squares solutions for estimating the average centre of rotation and the axis of rotation a new method is proposed for estimating the parameters of ball joints also known as spherical or revolute joints and hinge joints with a fixed axis of rotation the method does not require manual adjustment of any optimisation parameters and produces closed form solutions it is a least squares solution using the whole 3d motion data set we do not assume strict rigidity but only that the markers maintain a constant distance from the centre or axis of rotation this method is compared with other methods that use similar assumptions in the cases of random measurement errors systematic skin movements and skin movements with random measurement noise simulation results indicate that the new method is superior in terms of the algorithm used the closure of the solution consistency and minimal manual parameter adjustment the method can also be adapted to joints with translational movements

free vibration of thick layered rectangular plates with point supports by finite layer method in this paper the free vibration of thick isotropic and laminated composite rectangular plates with point supports is analyzed by the finite layer method a new set of two dimensional basic functions which satisfies the kinematic boundary conditions at the edges of the plate and the zero displacement conditions at point supports is developed to describe the variation of three dimensional displacements in the plane of a thin finite layer one dimensional linear or quadratic shape functions are adopted to describe the variation of the displacements through the thickness layer the governing eigenvalue equation of the plate is derived via the conventional displacement method numerical results for the three dimensional vibration of rectangular plates with point supports are presented herein for the first time the eigenfrequencies of simply supported rectangular plates with a central point support are studied in detail by considering the variations of aspect ratio side to thickness ratio properties of materials number of laminates and stacking sequences comparison with known thin plate and mindlin plate solutions is carried out to verify the applicability and accuracy of the proposed method

approximate solution for free vibrations of thin orthotropic rectangular plates abstract in this paper the problem of approximate evaluation of the frequencies of orthotropic plates is investigated starting from a general approximate formula for the frequency proposed by hearmon it is shown how to calculate the fundamental mode of an orthotropic rectangular plate with different restraint conditions using the proper coefficient values already available in the scientific literature for the higher modal frequencies a particular form of the rayleigh method is proposed leading to a simple procedure to calculate the fundamental frequency in fact the frequency calculation is reduced to the evaluation of the fundamental frequency of a special plate associated to the real one in order to test the accuracy of the proposed method an extensive finite element investigation was carried out the numerical results obtained show that the average difference between the values computed with the approximate new method and the finite element values is less than 0 74

robust estimation of dominant axis of rotation a simple method is developed for robustly estimating a fixed dominant axis of rotation aor of anatomical joints from surface marker data previous approaches which assume a model of circular marker trajectories use plane fitting to estimate the direction of the aor however when there is limited joint range of motion and rotation due to a second degree of freedom minimizing only the planar error can give poor estimates of the aor direction optimizing a cost function which includes the error component within a plane instead of only the component orthogonal to a plane leads to improved estimates of the aor direction for joints which exhibit additional rotational motion from a second degree of freedom results from synthetic data validation show the ranges of motion where the new method has lower estimation error compared to plane fitting techniques estimates of the flexion extension aor from empirical motion capture data of the knee and index finger joints were also more anatomically plausible

constrained least squares optimization for robust estimation of center of rotation this paper presents a new direct method for estimating the average center of rotation cor an existing least squares ls solution has been shown by previous works to have reduced accuracy for data with small range of motion rom alternative methods proposed to improve the cor estimation use iterative algorithms however in this paper we show that with a carefully chosen normalization scheme constrained least squares solutions can perform as well as iterative approaches even for challenging problems with significant noise and small rom in particular enforcing the normalization constraint avoids poor fits near plane singularities that can affect the existing ls method our formulation has an exact solution accounts for multiple markers simultaneously and does not depend on manually adjusted parameters simulation tests compare the method to four published cor estimation techniques the results show that the new approach has the accuracy of the iterative methods as well as the short computation time and repeatability of a least squares solution in addition application of the new method to experimental motion capture data of the thumb carpometacarpal cmc joint yielded a more plausible cor location compared to the previously reported ls solution and required less time than all four alternative techniques

the effect on conventional gait model kinematics and kinetics of hip joint centre equations in adult healthy gait abstract the conventional gait model cgm needs to benefit from large investigations on localization of the hip joint centre hjc incorrect positions from the native equations were demonstrated sangeux et al 2014 harrington et al 2007 more accurate equations were proposed but their impact on kinematics and kinetic cgm outputs was never evaluated this short communication aims at examining if adoption of new hjc equations would alter standard cgm outputs sixteen able bodied participants underwent a full 3 d optoelectronic gait analysis followed by a 3 d ultrasound localization of their hips data were processed through the open source python package pycgm2 replicating kinematic and kinetic processing of the native cgm compared with 3d ultrasound location hara equations improved the accuracy of sagittal plane kinematics 0 6 and kinetics 0 02 n m kg 1 for the hip the worst case participant exhibited harrington s equations reached a deviation of 3 for the sagittal kinematics in the coronal plane hara and harrington equations presented similar differences 1 for the hip whilst davis equations had the largest deviation for hip abduction 2 7 and hip abductor moment 0 10 n m kg 1 both harrington and hara equations improved the cgm location of the hjc hara equations improved results in the sagittal plane plus utilise a single anthropometrics measurement leg length that may be more robust however neither set of equations had significant effect on kinematics we reported some effects on kinetics particularly in the coronal plane which warrant caution in interpreting outputs using different sets of equations

a new method for estimating the axis of rotation and the center of rotation a new method is presented for estimating the parameters of two different models of a joint the two models are 1 a rotational joint with a fixed axis of rotation also referred to as a hinge joint and 2 a ball and socket model corresponding to a spherical joint given the motion of a set of markers it is shown how the parameters can be estimated utilizing the whole data set the parameters are estimated from motion data by minimizing two objective functions the method does not assume a rigid body motion but only that each marker rotates around the same fixed axis of rotation or center of rotation simulation results indicate that in situations where the rigid body assumption is valid and when measurement noise is present the proposed method is inferior to methods that utilize the rigid body assumption however when there are large skin movement artefacts simulation results show the proposed method to be more robust

the trace formula for vector bundles ii fedn x e i i j k is a tempered distributional function of t the classical trace formula says that the singular support of ii is contained in the length spectrum of x moreover under suitable hypotheses on geodesic flow the trace formula gives considerable information about the singularities in ii see dg and c there is a fairly straightforward and not terribly interesting generalization of the trace formula to vector bundles see for instance the introduction to dg we will be concerned in this article with a much more subtle generalization inspired by recent articles of hogreve potthoff and schrader hps and schrader and taylor st in communications in mathematical physics let g be a compact lie group and ir p x a principle g bundle with connection given a finite dimensional unitary representation p of g we will denote by ep the vector bundle over x associated with p and by dp the associated connection now consider a ladder pe e 1 2 of irreducible representations of g this means that the maximal weight of pe is e times the maximal weight of p for given e let afc e 1 2 o be the spectrum of the laplace operator on c epe ae d pedpe e

semiclassical spectra of gauge fields abstract we study the asymptotic behavior of the eigenvalues of the schrodinger operator with a vector potential on a compact manifold as planck s constant tends to zero we obtain estimates in terms of periodic trajectories of wong s flow which are uniform in the charge parameter

comparative evaluation of scapular and humeral coordinate systems based on biomedical images of the glenohumeral joint bio imaging techniques represent a powerful tool for shoulder joint biomechanical analysis however the restricted field of view may prevent the acquisition of complete scapula and humerus bone models and hence limiting the applicability of standardized anatomical coordinate system acs definitions the aim of this study was to propose acs definitions for both scapula and humerus which can be implemented when limited portions of the relevant bones are available magnetic resonance mr images of twenty right humeri and scapulae were acquired the proposed acss were assessed in terms of 1 sensitivity to bone morphological variation 2 intra and inter operator repeatability and 3 consistency with the anatomical cardinal directions a comparison with alternative acs definitions was also performed overall our acs scapular proposal and that presented in kedgley and dunning 2010 were found to be the least sensitive to the morphometric variability mean angular absolute deviation lower than 8 3 deg and they were characterized by a high intra and inter operator repeatability mean angular absolute deviation lower than 1 5 deg the humeral acs proposal showed a morphometric variability similar to amadi et al 2009b mean angular absolute deviation lower than 8 3 deg but a higher reproducibility the scapular and humeral acs mean angular deviation from the reference anatomical cardinal directions were smaller than 15 deg and 8 6 deg respectively the proposed scapular and humeral acs definitions are therefore suitable to be applied when a limited portion of the glenohumeral joint is available as it may occur in standard shoulder clinical exams

spinal shape changes resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation this paper reports the changes in spinal shape resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation the objective is to test the hypothesis that the type of spinal instrumentation system cotrel dubousset versus colorado does not influence these motion parameters intervertebral rotations and centers of rotation of the scoliotic spines were computed from the pre and post operative radiographs of 82 patients undergoing spinal correction the three dimensional 3d reconstruction of six anatomical landmarks was achieved for each of the thoracic and lumbar vertebrae a least squares approach based on singular value decomposition was used to calculate the rigid body transformation parameters average centers of rotation for all intervertebral levels are located in the neural canal at the mid sagittal plane and approximately at the superior endplate level of the inferior vertebra intervertebral rotations have components in all planes 6 7 degrees frontal 5 5 degrees sagittal and 4 5 degrees transverse rms for all intervertebral levels nearly all intervertebral rotations and centers of rotation are not significantly different for the two instrumentation systems various intervertebral rotations and 3d reconstruction errors were simulated on a theoretical model of a lumbar functional unit to assess the proposed method intervertebral rotation errors were 1 7 degrees when simulating 3d errors of 3mm on the position of the landmarks maximum errors for the position of centers of rotation were below 1cm in the case of intervertebral rotations larger than 2 5 degrees most cases but were larger 38 mm for small intervertebral rotations 1 degrees the type of instrumentation system did not influence intervertebral rotations and centers of rotation these results provide valuable data for the development and validation of simulation models for surgical instrumentation of idiopathic scoliosis

natural frequencies of orthotropic rectangular plates obtained by iterative reduction of the partial differential equation natural frequencies of orthotropic rectangular plates are obtained by successive reduction of the plate partial differential equation and by solving the resulting ordinary differential equation exactly the reduction of the partial differential equation is carried out by assuming an approximate solution satisfying the boundary conditions along one direction and employing a galerkin averaging technique known as the kantorovich method the resulting ordinary differential equation along the other direction is solved exactly which provides the natural frequencies of the plate natural frequencies of the orthotropic rectangular plates with various boundary conditions are obtained by using this approach and presented along with the discussion of the convergence and accuracy of the results

semi classical limit for random walks let g u be a discrete symmetric random walk on a compact lie group g with step distribution and let t be the associated transition operator on l2 g the irreducibles vp of the left regular representation of g on l2 g are finite dimensional invariant subspaces for t and the spectrum of t is the union of the sub spectra a t 1vp on the irreducibles which consist of real eigenvalues apl ap dim vp our main result is an asymptotic expansion for the spectral measures dim vp m dim vp j along rays of representations in a positive weyl chamber t i e for sequences of representations kp k c n with k oo as a corollary we obtain some estimates on the spectral radius of the random walk we also analyse the fine structure of the spectrum for certain random walks on u n for which tm is essentially a direct sum of harper operators

a correction for axis misalignment in the joint angle curves representing knee movement in gait analysis this paper derives a simple mathematical model relating changes in the orientations of the two cartesian coordinate systems involved in recording knee movement and the varus valgus and the internal external rotation angles for describing the knee s motion rotation matrices are given for changing the orientations of the two cartesian coordinate systems in such a way that the quadratic variations in the varus valgus and in the external internal angles are minimal these estimated rotation matrices are used to correct for axis misalignment the correction is calibrated by considering the impact of the new orientation of the thigh cartesian coordinate system on the hip joint angles the procedure is applied to kinematic data collected on normal subjects the uncertainty about the specification of the thigh cartesian coordinate system is shown to explain some of the between subject variability in the varus valgus and in the internal external rotation angles curves

in vivo estimation of the glenohumeral joint centre by functional methods accuracy and repeatability assessment abstract several algorithms have been proposed for determining the centre of rotation of ball joints these algorithms are used rather to locate the hip joint centre few studies have focused on the determination of the glenohumeral joint centre however no studies have assessed the accuracy and repeatability of functional methods for glenohumeral joint centre this paper aims at evaluating the accuracy and the repeatability with which the glenohumeral joint rotation centre ghrc can be estimated in vivo by functional methods the reference joint centre is the glenohumeral anatomical centre obtained by medical imaging five functional methods were tested the algorithm of gamage and lasenby 2002 bias compensated halvorsen 2003 symmetrical centre of rotation estimation ehrig et al 2006 normalization method chang and pollard 2007 helical axis woltring et al 1985 the glenohumeral anatomical centre ghac was deduced from the fitting of the humeral head four subjects performed three cycles of three different movements flexion extension abduction adduction and circumduction for each test the location of the glenohumeral joint centre was estimated by the five methods analyses focused on the 3d location on the repeatability of location and on the accuracy by computing the euclidian distance between the estimated ghrc and the ghac for all the methods the error repeatability was inferior to 8 25 mm this study showed that there are significant differences between the five functional methods the smallest distance between the estimated joint centre and the centre of the humeral head was obtained with the method of gamage and lasenby 2002

classical limits for quantum particles in external yang mills potentials we consider the limit 0 for nonrelativistic quantum particles moving in external yang mills potentials it is shown that the partition function and the solutions of the equations of motion converge to their corresponding classical counterparts

double calibration an accurate reliable and easy to use method for 3d scapular motion analysis the most recent non invasive methods for the recording of scapular motion are based on an acromion marker am set and a single calibration sc of the scapula in a resting position however this method fails to accurately measure scapular kinematics above 90 of arm elevation due to soft tissue artifacts of the skin and muscles covering the acromion the aim of this study was to evaluate the accuracy and inter trial and inter session repeatability of a double calibration method dc in comparison with sc the sc and dc data were measured with an optoelectronic system during arm flexion and abduction at different angles of elevation 0 180 they were compared with palpation of the scapula using a scapula locator dc data was not significantly different from palpation for 5 6 axes of rotation tested y x and z in abduction and flexion where as sc showed significant differences for 5 6 axes the root mean square errors ranged from 2 96 to 4 48 for dc and from 6 to 9 19 for sc the inter trial repeatability was good to excellent for sc and dc the inter session repeatability was moderate to excellent for sc and moderate to good for dc coupling am and dc is an easy to use method which yields accurate and reliable measurements of scapular kinematics for the complete range of arm motion it can be applied to the measurement of shoulder motion in many fields sports orthopaedics and rehabilitation especially when large ranges of arm motion are required

circular symmetry and the trace formula let m be a compact n dimensional manifold without boundary and let p be a positive first order elliptic self adjoint classical pseudodifferential operator on lz m the hilbert space of half densities on m the spectrum of p is discrete and accumulates only at we denote the eigenvalues with multiplicities by 2o 21 2 recall that the singularities of the inverse fourier transform of the spectral measure