Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers

1975 ◽  
Vol 42 (3) ◽  
pp. 552-556 ◽  
Author(s):  
A. J. Padgaonkar ◽  
K. W. Krieger ◽  
A. I. King
Keyword(s):  
Experimental Data ◽  
Rigid Body ◽  
Simple Procedure ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Theory And Practice ◽  
Body Segments ◽  
Impact Biomechanics ◽  
The Stability ◽  
Definition Of

The computation of angular acceleration of a rigid body from measured linear accelerations is a simple procedure, based on well-known kinematic principles. It can be shown that, in theory, a minimum of six linear accelerometers are required for a complete definition of the kinematics of a rigid body. However, recent attempts in impact biomechanics to determine general three-dimensional motion of body segments were unsuccessful when only six accelerometers were used. This paper demonstrates the cause for this inconsistency between theory and practice and specifies the conditions under which the method fails. In addition, an alternate method based on a special nine-accelerometer configuration is proposed. The stability and superiority of this approach are shown by the use of hypothetical as well as experimental data.

Computation of Rigid-Body Rotation in Three-Dimensional Space From Body-Fixed Linear Acceleration Measurements

1979 ◽  
Vol 46 (4) ◽  
pp. 925-930 ◽  
Author(s):  
N. K. Mital ◽  
A. I. King
Keyword(s):  
Rigid Body ◽  
High Speed ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Angular Acceleration ◽  
Linear Acceleration ◽  
Field Measurements ◽  
Moving Frame ◽  
Accelerometer Data ◽  
Hypothetical Data

The angular acceleration of a rigid body with respect to a body-fixed (moving) frame can be reliably computed from nine acceleration field measurements. Noncommutativity of finite rotations causes computational problems during numerical integration to obtain the transformation matrix, especially when the rotation is three-dimensional and there are errors in the measured linear accelerations. A method based on the orientation vector concept is formulated and tested against hypothetical data. The rigid-body rotations computed from linear accelerometer data from impact acceleration tests are compared against those obtained from three-dimensional analysis of high speed movie films.

scholarly journals A multi-physics analysis for the actuation of the SSS in opal reactor

2018 ◽  
Vol 4 ◽  
pp. 8
Author(s):  
Diego Ferraro ◽  
Patricio Alberto ◽  
Eduardo Villarino ◽  
Alicia Doval
Keyword(s):  
Experimental Data ◽  
Heavy Water ◽  
Research Reactor ◽  
Three Dimensional ◽  
Water Drainage ◽  
Hydraulic Behaviour ◽  
Component Design ◽  
Definition Of ◽  
Safety Features ◽  
Temporal Profiles

OPAL is a 20 MWth multi-purpose open-pool type Research Reactor located at Lucas Heights, Australia. It was designed, built and commissioned by INVAP between 2000 and 2006 and it has been operated by the Australia Nuclear Science and Technology Organization (ANSTO) showing a very good overall performance. On November 2016, OPAL reached 10 years of continuous operation, becoming one of the most reliable and available in its kind worldwide, with an unbeaten record of being fully operational 307 days a year. One of the enhanced safety features present in this state-of-art reactor is the availability of an independent, diverse and redundant Second Shutdown System (SSS), which consists in the drainage of the heavy water reflector contained in the Reflector Vessel. As far as high quality experimental data is available from reactor commissioning and operation stages and even from early component design validation stages, several models both regarding neutronic and thermo-hydraulic approaches have been developed during recent years using advanced calculations tools and the novel capabilities to couple them. These advanced models were developed in order to assess the capability of such codes to simulate and predict complex behaviours and develop highly detail analysis. In this framework, INVAP developed a three-dimensional CFD model that represents the detailed hydraulic behaviour of the Second Shutdown System for an actuation scenario, where the heavy water drainage 3D temporal profiles inside the Reflector Vessel can be obtained. This model was validated, comparing the computational results with experimental measurements performed in a real-size physical model built by INVAP during early OPAL design engineering stages. Furthermore, detailed 3D Serpent Monte Carlo models are also available, which have been already validated with experimental data from reactor commissioning and operating cycles. In the present work the neutronic and thermohydraulic models, available for OPAL reactor, are coupled by means of a shared unstructured mesh geometry definition of relevant zones inside the Reflector Vessel. Several scenarios, both regarding coupled and uncoupled neutronic & thermohydraulic behavior, are presented and analyzed, showing the capabilities to develop and manage advanced modelling that allows to predict multi-physics variables observed when an in-depth performance analysis of a Research Reactor like OPAL is carried out.

scholarly journals SUSTAINABILITY OF THE FINANCIAL SYSTEM OF THE REGION: ISSUES OF THEORY AND PRACTICE

2020 ◽  
pp. 95-102
Author(s):  
О.В. Гончарук ◽  
Ю.Е. Путихин
Keyword(s):  
Financial Stability ◽  
Financial System ◽  
Financial Sector ◽  
Theory And Practice ◽  
Practical Significance ◽  
Insurance Companies ◽  
Municipal Finance ◽  
The Russian Federation ◽  
The Stability ◽  
Definition Of

В статье с позиций общего методологического анализа понятия «устойчивость» обоснована теоретическая и практическая значимость использования понятия «устойчивость финансовой системы региона», проанализированы подходы к раскрытию особенностей понятий финансовой устойчивости нефинансовых организаций, банков и страховых компаний, проанализированы подходы к определению понятия финансовой системы страны/ региона и ее структуры. В качестве основополагающего для целей анализа устойчивости финансовой системы региона выбран подход, в рамках которого финансовая система региона рассматривается как совокупность взаимодействующих и взаимосвязанных между собой таких секторов как сектор государственных и муниципальных финансов, финансовый сектор региона, региональный сектор корпоративных и личных финансов. Показана неравномерность развития отдельных институтов финансового сектора Российской Федерации и проанализированы основные показатели развития секторов финансовой системы страны за период 2016-2020 гг. Изложены методические подходы Банка России к исследованию финансовой стабильности. Предложено авторское определение «устойчивость финансовой системы региона» и совокупность параметров и показателей для оценки устойчивости секторов финансовой системы региона. The article substantiates the theoretical and practical significance of using the concept of "stability of the financial system of the region" from the standpoint of a general methodological analysis of the concept of "stability", analyzes approaches to revealing the features of the concepts of financial stability of non-financial organizations, banks and insurance companies, analyzes approaches to defining the concept of the financial system of a country / region and its structure; as a fundamental approach for the purposes of analyzing the stability of the financial system of the region, the approach is chosen in which the financial system of the region is considered as a set of interacting and interconnected sectors: the sector of state and municipal finance, the financial sector of the region, the regional sector of corporate and personal finance. The uneven development of individual institutions of the financial sector of the Russian Federation is shown and the main indicators of the development of the country's financial system sectors for the period 2016-2020 are analyzed. The methodological approaches of the Bank of Russia to the study of financial stability are described. The author's definition of "stability of the financial system of the region" and a set of parameters and indicators for assessing the stability of the financial system sectors of the region are proposed.

scholarly journals Post-Newtonian treatise on the rotational motion of a finite body

1986 ◽  
Vol 114 ◽  
pp. 35-40 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Angular Momentum ◽  
Rigid Body ◽  
Angular Acceleration ◽  
Relative Magnitude ◽  
The Body ◽  
Coordinate Systems ◽  
Functional Forms ◽  
Finite Body ◽  
The Moment ◽  
Definition Of

The definition of the angular momentum of a finite body is given in the post-Newtonian framework. The non-rotating and the rigidly rotating proper reference frame(PRF)s attached to the body are introduced as the basic coordinate systems. The rigid body in the post-Newtonian framework is defined as the body resting in a rigidly rotating PRF of the body. The feasibility of this rigidity is assured by assuming suitable functional forms of the density and the stress tensor of the body. The evaluation of the time variation of the angular momentum in the above two coordinate systems leads to the post-Newtonian Euler's equation of motion of a rigid body. The distinctive feature of this equation is that both the moment of inertia and the torque are functions of the angular velocity and the angular acceleration. The obtained equation is solved for a homogeneous spheroid suffering no torque. The post-Newtonian correction to the Newtonian free precession is a linear combination of the second, fourth and sixth harmonics of the precessional frequency. The relative magnitude of the correction is so small as of order of 10−23 in the case of the Earth.

Local Metrics for Rigid Body Displacements

2004 ◽  
Vol 126 (5) ◽  
pp. 805-812 ◽  
Author(s):  
Johannes K. Eberharter ◽  
Bahram Ravani
Keyword(s):  
Rigid Body ◽  
Projective Space ◽  
Affine Space ◽  
Three Dimensional ◽  
Real Space ◽  
Elegant Method ◽  
Rigid Body Displacement ◽  
Definition Of ◽  
Three Space ◽  
Motion Design

One hundred years ago, Eduard Study introduced a very elegant method to describe a rigid body displacement in three-space. He mapped each position of a rigid body onto a point on a quadric, now called the Study quadric. This quadric is a six-dimensional rational hyper-surface, embedded in a seven-dimensional projective real space, called Study’s soma space. More than half a century later Ravani and Roth reconfigured Study’s soma space into a three-dimensional dual projective space, and defined a geometric metric for rigid body displacements. Here, approximately 20 years later, we again use Study’s quadric and define a new metric for rigid body displacements based on an optimized local mapping of the quadric. The local mappings of the quadric are achieved using stereographic projections, resulting in an affine space where the Euclidean definition of a metric can be used for rigid body displacements and techniques from design of curves and surfaces can be directly utilized for motion design. The results are illustrated by examples.

scholarly journals The Torsional Stability of a Compressor Cascade

1991 ◽  
Author(s):  
M. R. D. Davies
Keyword(s):  
Experimental Data ◽  
Three Dimensional ◽  
Compressor Cascade ◽  
Influence Coefficients ◽  
Blade Row ◽  
The Stability ◽  
Torsional Stability

This paper includes new experimental data on the torsional stability of a compressor or fan type of blade row. This data is linked in with published material to form a three dimensional figure describing the stability of such rows. The data is then discussed by considering relative values of influence coefficients and some of the trends in the stability figure are explained. New data is also included on the relative magnitudes and phases of the influence coefficients.

Comparison of Digital and Conventional Radiostereometric Image Analysis in an Ankle Phantom Model

2005 ◽  
Vol 94 (3) ◽  
pp. 233-238 ◽  
Author(s):  
T. J. Mäkinen ◽  
K. T. Mattila ◽  
H. Määttänen ◽  
H. T. Aro
Keyword(s):  
Rigid Body ◽  
Three Dimensional ◽  
Relative Displacement ◽  
Radiostereometric Analysis ◽  
Body Segments ◽  
Phantom Model ◽  
Plain Films ◽  
Dimensional Measurements ◽  
The Mean ◽  
Scanned Images

Background and Aims: Radiostereometric analysis (RSA) allows accurate three-dimensional measurements of micromotion in skeletal structures. The current RSA techniques are based on the analysis of scanned plain films. This study was undertaken to compare digital filmless RSA technique to conventional scanning technique using a phantom model of the ankle mortise. Material and Methods: In the first experiment, the relative displacement of the markers inserted to the fibula in relation to the markers inserted to the tibia was studied by means of double examinations and the precision of DICOM images were compared to scanned images of printed radiographs. In the second experiment, the film pair of double examination was re-imported or re-scanned and self-compared in order to show merely the error related to the image processing. Results: The precision of RSA using scanned images of printed radiographs was compatible to DICOM images. However, the mean error of rigid body fitting (ME) values were significantly lower in use of DICOM images compared with scanned radiographs, indicating less deformation of rigid body segments in filmless analysis. Conclusions: Precision of the RSA method was improved under the completely filmless environment. Therefore, this technique can be recommended for clinical studies of radiostereometric analysis.

Simulation of the Onset of Rotating Stall

2001 ◽  
Author(s):  
Christopher J. Freitas ◽  
Anthony J. Smalley
Keyword(s):  
Experimental Data ◽  
Three Dimensional ◽  
Stability Limit ◽  
Rotating Stall ◽  
Time Dependent ◽  
Navier Stokes ◽  
Width Ratio ◽  
Threshold Condition ◽  
Flow Angle ◽  
The Stability

Abstract This paper presents the results of a series of numerical simulations exploring the stability of fluid flow in vaneless diffusers of centrifugal compressors. Three-dimensional, time-dependent, Reynolds-averaged Navier-Stokes simulations were performed for a fixed diffuser width ratio. Effective flow angle was varied from simulation to simulation in order to predict the threshold angle at which the instability — rotating stall — is manifested and maintained. The predicted threshold angle or stability limit is in excellent agreement with experimental data. The simulations reveal a two-stall cell configuration at the threshold condition.

GENERALIZED MANDELBROT SETS FOR MEROMORPHIC COMPLEX AND QUATERNIONIC MAPS

2002 ◽  
Vol 12 (08) ◽  
pp. 1755-1777 ◽  
Author(s):  
WALTER BUCHANAN ◽  
JAGANNATHAN GOMATAM ◽  
BONNIE STEVES
Keyword(s):  
Parameter Space ◽  
Three Dimensional ◽  
Mandelbrot Set ◽  
Rational Maps ◽  
Fractal Structures ◽  
Stability Regions ◽  
Theoretical Support ◽  
The Stability ◽  
Definition Of ◽  
Meromorphic Maps

The concepts of the Mandelbrot set and the definition of the stability regions of cycles for rational maps require careful investigation. The standard definition of the Mandelbrot set for the map f : z → z2+ c (the set of c values for which the iteration of the critical point at 0 remains bounded) is inappropriate for meromorphic maps such as the inverse square map. The notion of cycle sets, introduced by Brooks and Matelski [1978] for the quadratic map and applied to meromorphic maps by Yin [1994], facilitates a precise definition of the Mandelbrot parameter space for these maps. Close scrutiny of the cycle sets of these maps reveals generic fractal structures, echoing many of the features of the Mandelbrot set. Computer representations confirm these features and allow the dynamical comparison with the Mandelbrot set. In the parameter space, a purely algebraic result locates the stability regions of the cycles as the zeros of characteristic polynomials. These maps are generalized to quaternions. The powerful theoretical support that exists for complex maps is not generally available for quaternions. However, it is possible to construct and analyze cycle sets for a class of quaternionic rational maps (QRM). Three-dimensional sections of the cycle sets of QRM are nontrivial extensions of the cycle sets of complex maps, while sharing many of their features.

Three-dimensional disturbances in flow between parallel planes

1960 ◽  
Vol 254 (1279) ◽  
pp. 562-569 ◽  
Keyword(s):  
Reynolds Number ◽  
Dimensional Stability ◽  
Flow Direction ◽  
Simple Procedure ◽  
Three Dimensional ◽  
Stability Diagram ◽  
Wave Number ◽  
Two Dimensional ◽  
General Answer ◽  
The Stability

The close connexion between the stability of three-dimensional and two-dimensional disturbances in flow between parallel walls has been examined and this has led to the formation of a three-dimensional stability diagram where ‘stability surfaces’ replace stability curves. The problem which has been investigated is whether the most highly amplifying disturbance at any given Reynolds number above the minimum critical Reynolds number is a two-dimensional or a three-dimensional disturbance. It has been shown that the most unstable disturbance is a two-dimensional one for a certain definite range of Reynolds number above the critical. For Reynolds numbers greater than this no definite general answer has been found; each basic undisturbed flow must be treated separately and a simple procedure has been given which, in principle, determines the type of disturbance which is most unstable. Difficulty arises in following this procedure because it requires knowledge of the two-dimensional stability curves in a certain region where this knowledge is very scanty at the moment. Althoughth is difficulty arises, in Poiseuille flow the calculations available indicate very strongly that the most unstable disturbance at any given Reynolds number above the critical is two-dimensional. Further, it is believed that this result holds for all other basic flows. A second result is that if the wave number (a) in the flow direction is specified, as well as the Reynolds number, then for a in a certain range, the most unstable disturbance is three-dimensional.

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