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Academic literature on the topic 'Euler principal axis'
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Journal articles on the topic "Euler principal axis"
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Iz, H., C. Shum, X. Ding, and C. Dai. "Orientation of the Geometrically Best fitting Triaxial Lunar Ellipsoid with Respect to the Mean Earth/Polar Axis Reference Frame." Journal of Geodetic Science 1, no. 1 (March 1, 2011): 52–58. http://dx.doi.org/10.2478/v10156-010-0007-2.
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Orientation of the Geometrically Best fitting Triaxial Lunar Ellipsoid with Respect to the Mean Earth/Polar Axis Reference FrameThis study provides new estimates for the orientation of a geometrically best fitting lunar triaxial ellipsoid with respect to the mean Earth/polar axis reference frame calculated from the footprint positions of the Chang'E-1 (CE-1), SELenological and ENgineering Explorer (SELENE) laser altimetry measurements and Unified Lunar Control Networks 2005, (ULCN 2005) station coordinates. The semi-principal axes of the triaxial ellipsoid and the coordinates of its geometric center are also calculated simultaneously. All the estimated parameters from all three data sets are found to be consistent. In particular, the RMS differences of the semi-principal axes of the triaxial ellipsoids and the locations of their geometric centers from solutions with and without modeling Euler angles (orientation of the triaxial ellipsoid) using uniformly distributed laser altimetry (LAL) footprints are 29 and 31 m respectively. The misclosures of all the solutions indicate a better fit for the triaxial ellipsoid to the footprint and station coordinates if the Euler angles are included in the models.
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Yin, Changchun. "Inherent nonuniqueness in magnetotelluric inversion for 1D anisotropic models." GEOPHYSICS 68, no. 1 (January 2003): 138–46. http://dx.doi.org/10.1190/1.1543201.
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This paper investigates the inherent nonuniqueness in the inversion of magnetotelluric (MT) measurements over an earth with a layered anisotropic resistivity distribution. This kind of nonuniqueness arises from the fact that even accurate and complete data contain insufficient information to uniquely resolve the earth parameters. For a very simple anisotropic case, where all layers in the earth have at least one horizontal principal axis in common coinciding with the x‐ or y‐axis of the Cartesian coordinate system, the resolvable parameters or parameter combinations from MT surface observations are identified by analyzing the structure of the conductivity tensor of the earth and the differential equations the electromagnetic (EM) fields satify. It is found that for a layered anisotropic earth model, several parameters can be uniquely resolved from the MT inversion while others are nonresolvable. However, particular combinations of the nonresolvable parameters can be uniquely resolved. These theoretical findings on the parameter resolvability of MT anisotropic inversion are further verified by a number of numerical experiments using synthetic data and a nonlinear parameter estimation technique. For this purpose, I parameterize the resistivity tensor assigned to each layer of the earth with three principal resistivities and three Euler angles, and then use the three Euler angles, the logarithms of three principal resistivities, and the logarithmic thickness as inverse parameters. This guarantees that the layer thickness is positive and the resistivity tensor is positive‐definite, while at the same time the inverse parameters may span the whole real axis. Numerical inversion results for different anisotropic models also reveal the fact that the resolvable parameters and parameter combinations are invariant with respect to the starting model. This means that for different starting models, the inversion results for some earth parameters might be individually quite different; however, particular combinations of these parameters remain unchanged.
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Li, Yan Bin, Ren Song Zou, and Tong Jiang. "Influence on Inertia the Moment of Inertia Matrix of Three Degrees of Freedom Air-Bearing Testbed." Advanced Materials Research 706-708 (June 2013): 1393–96. http://dx.doi.org/10.4028/www.scientific.net/amr.706-708.1393.
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To improve the accuracy of attitude determination and control stabilization when simulating attitude motion of satellites in the space, the finite element model of the platform of 3-DOF spacecraft attitude control simulator was founded. Gravity field of air bearing testbed and formula for platform’s moment of inertia on the action of gravity was induced The result shows platform’s attitude accuracy error exist because of main principal axis of inertia change of direction.on the action of gravity, The more large value it is, the more error is .Error of inertia main axis changes as sine curve with the change of two horizontal Euler angle.
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Sun, Xiaofeng, Liang Tao, Yuanzhe Zhao, Jingyu Qu, Di Yao, and Zijian Li. "Numerical Simulation of Hole Cleaning of a Horizontal Wellbore Model with Breakout Enlargement Section." Mathematics 11, no. 14 (July 12, 2023): 3070. http://dx.doi.org/10.3390/math11143070.
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Horizontal wells are more likely than vertical wells to have enlarged wellbore sections due to borehole instability. However, there is scarce research on borehole cleaning of horizontal wells with enlarged wellbore sections. In this paper, we establish a horizontal wellbore model with a breakout enlargement section using field borehole diameter data. We used the three-dimensional computational fluid dynamics (CFD) method and the Realizable k-ε turbulence model with the Euler–Euler approach to simulate the effects of the drilling fluid circulation return speed and the spinning speed of the drill pipe on the cutting movement of conventional horizontal wells and horizontal wells with a breakout enlargement section. The simulation results demonstrate that increasing the drilling fluid circulation return speed and the spinning speed of the drill pipe does not significantly improve the hole cleaning impact for horizontal wells with a breakout enlargement section. We analyzed the effects of the enlargement ratio, ellipticity, and principal axis orientation on the borehole cleaning effect of horizontal wells with a breakout enlargement section. The results show that the cleaning impact is better when the enlargement ratio is lower; moreover, the ellipticity is larger and the principal axis orientation is perpendicular to the gravity direction. This paper fills a gap in the existing theory of hole cleaning in horizontal wells and provides a theoretical basis for improving the hole cleaning effect in actual drilling processes.
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Wu, Jianwei, Fuyun Liu, Yong Deng, and Lin Gan. "Calculation of the principal moment of inertia and Euler angles of the centre inertia principal axis system: design and implementation of the algorithm." International Journal of Materials and Structural Integrity 9, no. 1/2/3 (2015): 180. http://dx.doi.org/10.1504/ijmsi.2015.071119.
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Nyaban, Christian Emile, Théophile Ndougsa-Mbarga, Marcelin Bikoro-Bi-Alou, Stella Amina Manekeng Tadjouteu, and Stephane Patrick Assembe. "Multi-scale analysis and modelling of aeromagnetic data over the Bétaré-Oya area in eastern Cameroon, for structural evidence investigations." Solid Earth 12, no. 4 (April 6, 2021): 785–800. http://dx.doi.org/10.5194/se-12-785-2021.
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Abstract. This study was carried out in the Lom series in Cameroon, at the border with Central African Republic, located between the latitudes 5∘30′–6∘ N and the longitudes 13∘30′–14∘45′ E. A multi-scale analysis of aeromagnetic data combining tilt derivative, Euler deconvolution, upward continuation, and 2.75D modelling was used. The following conclusions were drawn. (1) Several major families of faults were mapped. Their orientations are ENE–WSW, E–W, NW–SE, and N–S with a NE–SW prevalence. The latter are predominantly sub-vertical with NW and SW dips and appear to be prospective for future mining investigations. (2) The evidence of compression, folding, and shearing axis was concluded from superposition of null contours of the tilt derivative and Euler deconvolution. The principal evidence of the local tectonics was due to several deformation episodes (D1, D2, and D4) associated with NE–SW, E–W, and NW–SE events, respectively. (3) Depths of interpreted faults range from 1000 to 3400 m. (4) Several linear structures correlating with known mylonitic veins were identified. These are associated with the Lom faults and represent the contacts between the Lom series and the granito-gneissic rocks; we concluded the intense folding was caused by senestral and dextral NE–SW and NW–SE stumps. (5) We propose a structural model of the top of the crust (schists, gneisses, granites) that delineates principal intrusions (porphyroid granite, garnet gneiss, syenites, micaschists, graphite, and garnet gneiss) responsible for the observed anomalies. The 2.75D modelling revealed many faults with a depth greater than 1200 m and confirmed the observations from reduced-to-Equator total magnetic intensity (RTE-TMI), tilt derivative, and Euler deconvolution. (6) We developed a lithologic profile of the Bétaré-Oya basin.
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Ferretti, Roberta, and Silvana G. Dellepiane. "Multitemporal Volume Registration for the Analysis of Rheumatoid Arthritis Evolution in the Wrist." International Journal of Biomedical Imaging 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/7232751.
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This paper describes a method based on an automatic segmentation process to coregister carpal bones of the same patient imaged at different time points. A rigid registration was chosen to avoid artificial bone deformations and to allow finding eventual differences in the bone shape due to erosion, disease regression, or other eventual pathological signs. The actual registration step is performed on the basis of principal inertial axes of each carpal bone volume, as estimated from the inertia matrix. In contrast to already published approaches, the proposed method suggests splitting the 3D rotation into successive rotations about one axis at a time (the so-called basic or elemental rotations). In such a way, singularity and ambiguity drawbacks affecting other classical methods, for instance, the Euler angles method, are addressed. The proposed method was quantitatively evaluated using a set of real magnetic resonance imaging (MRI) sequences acquired at two different times from healthy wrists and by choosing a direct volumetric comparison as a cost function. Both the segmentation and registration steps are not based on a priori models, and they are therefore able to obtain good results even in pathological cases, as proven by the visual evaluation of actual pathological cases.
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Krasavin, V. V., and A. V. Krasavin. "Study of the elastic properties of hexagonal metal single crystals." Industrial laboratory. Diagnostics of materials 85, no. 9 (September 28, 2019): 29–35. http://dx.doi.org/10.26896/1028-6861-2019-85-9-29-35.
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Hexagonal metals (e.g., Be, Zr, Ti) are widely used in the nuclear industry, space and aircraft engineering (in manufacturing of the structural elements operating under extreme conditions). A promising way to improve the quality of products made of them is to improve the physical properties of materials using the natural anisotropy of metal single crystals. The results of studying anisotropy and a comparative analysis of the technical characteristics of the elastic properties of single crystals of hexagonal metals are presented. The equations of the elastic compliance matrix components are derived in the explicit form for arbitrary crystallographic direction proceeding from transformations of the elastic compliance tensor in the principal axes to a new arbitrary coordinate system with a subsequent use of Euler angles. Analytical expressions are presented for the technical characteristics of the elastic properties (shear and Young's moduli, Poisson's ratio) of the single crystals of 10 hep metals for an arbitrary crystallographic direction. The axial symmetry of the characteristics about the hexagonal axis is revealed. The sums of the elastic compliance coefficients which determine the shear moduli and the Poisson's ratios in two mutually perpendicular directions are constant in any crystallographic plane of the single crystal. A comparative analysis of the anisotropy of the elastic properties of single crystals of the studied group of metals revealed auxetic properties of Zn and Be single crystals and the region of crystallographic directions of uniaxia tension, leading to an auxetic effect The auxetic effect in Zn was observed under tension in the directions of the plane perpendicular to the hexagonal axis of the single crystal. The planes of the auxetic effect manifestation in Be single crystals are perpendicular to the directions making an angle of 45° with the hexagonal axis.
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Adiga, Samyuktha, Dominic Aebi, and David L. Bryce. "EFGShield — A program for parsing and summarizing the results of electric field gradient and nuclear magnetic shielding tensor calculations." Canadian Journal of Chemistry 85, no. 7-8 (July 1, 2007): 496–505. http://dx.doi.org/10.1139/v07-069.
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A computer program (EFGShield) is described that simplifies and summarizes the output from electric field gradient (EFG) and nuclear magnetic shielding tensor calculations performed independently using existing quantum chemical software. In addition to summarizing tensor magnitudes according to conventions commonly used by solid-state NMR spectroscopists, the program provides Euler angles relating the orientations of the EFG and shielding tensor principal axis systems (PAS). An atomic coordinate file is generated that also contains dummy atoms representing the orientations of the EFG and shielding tensor PASs in the molecular framework. We demonstrate the functionality of the program using calculations of the chlorine EFG and shielding tensors for strontium chloride dihydrate and calcium chloride dihydrate. Several models of the chloride environment in these compounds are tested, including those where point charges are used to represent the extended three-dimensional lattices within the self-consistent charge field perturbation approach. The results highlight both the shortcomings and successes of traditional localized orbital-based basis sets in the description of the NMR properties of extended systems. We anticipate that EFGShield will be a useful tool for spectroscopists using quantum chemical software to aid in the interpretation of experimental data.Key words: quantum chemical calculations, computer program, electric field gradient tensor, quadrupolar coupling constant, nuclear magnetic shielding tensor, Euler angles, alkaline earth chloride hydrates.
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Carretero, Paula, and Ildefonso Castro. "A New Approach to Rotational Weingarten Surfaces." Mathematics 10, no. 4 (February 12, 2022): 578. http://dx.doi.org/10.3390/math10040578.
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Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane curve, we propose a new approach to the study of rotational Weingarten surfaces in Euclidean 3-space. Our contribution consists of reducing any type of Weingarten condition on a rotational surface to a first-order differential equation on the momentum of the generatrix curve. In this line, we provide two new classification results involving a cubic and an hyperbola in the W-diagram of the surface characterizing, respectively, the non-degenerated quadric surfaces of revolution and the elasticoids, defined as the rotational surfaces generated by the rotation of the Euler elastic curves around their directrix line. As another application of our approach, we deal with the problem of prescribing mean or Gauss curvature on rotational surfaces in terms of arbitrary continuous functions depending on distance from the surface to the axis of revolution. As a consequence, we provide simple new proofs of some classical results concerning rotational surfaces, such as Euler’s theorem about minimal ones, Delaunay’s theorem on constant mean curvature ones, and Darboux’s theorem about constant Gauss curvature ones.
Conference papers on the topic "Euler principal axis"
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Chembrammel, Pramod, and Thenkurussi Kesavadas. "A Novel Method to Model the Dynamics of an Uniball Robot." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38641.
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In this paper the kinematics and dynamics of a uniball robot is demonstrated. The motion of a uniball robot is derived from the dynamics of a sphere rolling on a surface which is considered as a motion about a fixed point. The equations of motion are derived using Newton-Euler method incorporating the geometrical features of the surface. A uniball-robot can be considered as a Routh’s sphere whose center of mass is not at the geometrical center and have equal principal moments of inertia in the plane perpendicular to the axis connecting the center of mass and the geometrical center. The Euler angles are obtained using the Meusnier’s theorem which deals with the evolution of the surface as the robot moves along.
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Murakami, Hidenori, Oscar Rios, and Thomas J. Impelluso. "A Theoretical and Numerical Study of the Dzhanibekov and Tennis Racket Phenomena." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52374.
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In this paper, we present complete explanation of the Dzhanibekov phenomenon demonstrated in a space station (www.youtube.com/watch?v=L2o9eBl_Gzw) and the tennis racket phenomenon (www.youtube.com/watch?v=4dqCQqI-Gis). These phenomena are described by Euler’s equation of an unconstrained rigid body that has three distinct values of moments of inertia. In the two phenomena, the rotations of a body about the principal axes that correspond to the largest and the smallest moments of inertia are stable. However, the rotation about the axis corresponding to the intermediate principal moment of inertia becomes unstable, leading to the unexpected rotations that are the basis of the phenomena. If this unexpected rotation is not explained from a complete perspective which accounts for the relevant physical and mathematical aspects, one might misconstrue the phenomena as a violation of the conservation of angular momenta. To address this, especially for students, we investigate the phenomena using more precise mathematical and graphical tools than those employed previously. Following Élie Cartan [1], we explicitly write the vector basis of a body-attached, moving coordinate system. Using this moving frame method, we describe the Newton and Euler equations. The adoption of the moving coordinate frame expresses the rotation of the body more clearly and allows us to use the Lie group theory of special orthogonal group SO(3). We integrate the torque-free Euler equation using the fourth-order Runge-Kutta method. Then we apply a recovery equation to obtain the rotation matrix for the body. By combining the geometrical solutions with numerical simulations, we demonstrate that the unexpected rotations observed in the Dzhanibekov and the tennis racket experiments preserve the conservation of angular momentum.
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Du, S. J., M. Kalveram, and K. Weinert. "Dynamic Modeling and Simulation of Parallel Kinematic Machines." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57163.
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This paper presents an effective method for inverse dynamic modeling of a five-axis milling machine with parallel kinematic chains (PKM). For solving the inverse dynamics, the methodology of using the principle of virtual work is introduced, which corrects a theoretic error in formulating the dynamic equations of motions sound in previous literatures. A corresponding computational algorithm for solving the inverse dynamics of the parallel kinematic machine is given and two cases of motion trajectories are calculated to check the proposed method. The corrected dynamic modeling is robust and features higher computational efficiency than other dynamic modeling methods such as recursive Newton-Euler method or Lagrangian formulations. Using this dynamic modeling and simulation method, we can anticipate the dynamic behavior of the five-axis machine and develop a suitable algorithm for motion control and dynamic optimization.
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Hilton, Harry H. "Sensitivity Analyses for Viscoelastic Strength of Materials and Corresponding Continuum Mechanics Formulations." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68832.
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Comparison analyses are conducted for straight and curved viscoelastic beams based on Euler-Bernoulli strength of materials prescriptions and on rigorous formulations in terms of 3-D field equations. The concepts of elastic straight and curved beam analyses are well established. In the present paper, these geometric principles are extended to linear viscoelastic materials. The beams are considered subjected to un-symmetric bending as well as to thermal expansions. The distinct conditions leading to shear center and neutral axis motions in time, previously observed in straight beams are investigated. The applicability of the elastic-viscoelastic correspondence principle (analogy) in terms of integral transforms is demonstrated by application to several simulations. Comparison studies are based on pure bending loading configurations as these offer the least distinct geometric deformation patterns.
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Ubulom, Iroizan. "Application of Spectral Method for Vibration-Induced High-Cycle Fatigue Evaluation of an HP Turbine Blade." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14477.
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Abstract A method of fluid-structure interaction coupling is implemented for a forced-response, vibration-induced fatigue life estimation of a high-pressure turbine blade. Two simulations approaches; a two-way (fully-coupled) and one-way (uncoupled) methods are implemented to investigate the influence of fluidsolid coupling on a turbine blade structural response. The fatigue analysis is performed using the frequency domain spectral moments estimated from the response power spectral density of the two simulation cases. The method is demonstrated in light of the time-domain method of the rainflow cycle counting method with mean stress correction. Correspondingly, the mean stress and multiaxiality effects are also accounted for in the frequency domain spectral approach. In the mean stress case, a multiplication coefficient is derived based on the Morrow equation, while the case of multiaxiality is based on a criterion which reduces the triaxial stress state to an equivalent uniaxial stress using the critical plane assumption. The analyses show that while the vibration-induced stress histories of both simulation approaches are stationary, they violate the assumption of normality of the frequency domain approaches. The stress history profile of both processes can be described as platykurtic with the distributions having less mass near its mean and in the tail region, as compared to a Gaussian distribution with an equal standard deviation. The fully-coupled method is right leaning with positive skewness while the uncoupled approach is left leaning with negative skewness. The directional orientation of the principal axes was also analyzed based on the Euler angle estimation. Although noticeable differences were found in the peak distribution of the normal stresses for both methods, the predicted Euler angle orientations were consistent in both cases, depicting a similar orientation of the critical plane during a crack initiation process. It is shown that the fatigue life estimation was conservative in the fully-coupled solution approach.