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Journal articles on the topic 'Three-dimensional Polar Coordinates Representation'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Kaido, Takanobu, Tohru Hoshida, Toshiaki Taoka, and Toshisuke Sakaki. "Retinotopy with coordinates of lateral occipital cortex in humans." Journal of Neurosurgery 101, no. 1 (2004): 114–18. http://dx.doi.org/10.3171/jns.2004.101.1.0114.

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Object. The lateral occipital cortex in humans is known as the “extrastriate visual cortex.” It is, however, an unexplored field of research, and the anatomical nomenclature for its surface has still not been standardized. This study was designed to investigate whether the lateral occipital cortex in humans has retinotopic representation. Methods. Four right-handed patients with a diagnosis of intractable epilepsy from space-occupying lesions in the occipital lobe or epilepsy originating in the occipital lobe received permanently implanted subdural electrodes. Electrical cortical stimulation w

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Tenzer, Robert, and Vladislav Gladkikh. "Application of Möbius coordinate transformation in evaluating Newton's integral." Contributions to Geophysics and Geodesy 41, no. 2 (2011): 95–115. http://dx.doi.org/10.2478/v10126-011-0004-1.

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Application of Möbius coordinate transformation in evaluating Newton's integralWe propose a numerical scheme which efficiently combines various existing methods of solving the Newton's volume integral. It utilises the analytical solution of Newton's integral for tesseroid in computing the near-zone contribution to gravitational field quantities (potential and its first radial derivative). The far-zone gravitational contribution is computed using the expressions derived based on applying Molodensky's truncation coefficients to a spectral representation of Newton's integral. The weak singularity

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XU, TINGTING, PENGCHENG LI, SHANGBIN CHEN, and WEIHUA LUO. "TWO-DIMENSIONAL VISUALIZATION OF THE PROPAGATION SPEED OF CORTICAL SPREADING DEPRESSION IN RAT CORTEX." Journal of Innovative Optical Health Sciences 03, no. 01 (2010): 75–80. http://dx.doi.org/10.1142/s1793545810000873.

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Cortical spreading depression (CSD), which is a significant pathological phenomenon that correlates with migraines and cerebral ischemia, has been characterized by a wave of depolarization among neuronal cells and propagates across the cortex at a rate of 2–5 mm/min. Although the propagation pattern of CSD was well-investigated using high-resolution optical imaging technique, the variation of propagation speed of CSD across different regions of cortex was not well-concerned, partially because of the lack of ideal approach to visualize two-dimensional distribution of propagation speed of CSD ov

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Dinavahi, SL Divya, Jiangyi Chen, Paul R. Heyliger, and Ernian Pan. "Coupled fields in layered thermomagnetoelectroelastic spheres." Journal of Intelligent Material Systems and Structures 29, no. 13 (2018): 2782–94. http://dx.doi.org/10.1177/1045389x18778373.

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A discrete-layer model is presented and applied to layered anisotropic spheres with coupling among the elastic, electric, magnetic, and temperature fields under static conditions. The governing differential equations that represent these interactions are solved using a combination of one-dimensional finite element approximations in the radial direction with analytic functions over the polar and azimuthal coordinates of the sphere. This allows for an excellent representation of the type of variability in behavior across an interface between two dissimilar materials while keeping computational c

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Sekii, T., and D. O. Gough. "A Procedure For Two-Dimensional Asymptotic Rotational-Splitting Inversion." International Astronomical Union Colloquium 137 (1993): 569–71. http://dx.doi.org/10.1017/s0252921100018479.

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AbstractRotational splitting Δω(n,l,m) of the eigenfrequencies of a star rotating with angular velocity Ω(r, θ) about a unique axis can be represented as a weighted integral of Ω over r and θ, (r, θ, φ) being spherical polar coordinates about the axis of rotation. For high-frequency acoustic modes, Δω/m collapses essentially to a function of ω — ω /(l+1/2) and M = m/(l + 1/2) alone, and the weighting kernel K(r,θ) becomes asymptotically degenerate, each factor being of essentially Abel type. Therefore, formally, the splitting integral can be inverted, once a procedure has been found for extend

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Williams, Carol A. "A Planetary Theory with Elliptic Functions and Elliptic Integrals Exhibiting no Small Divisors." Symposium - International Astronomical Union 152 (1992): 43–48. http://dx.doi.org/10.1017/s0074180900090926.

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This paper develops a planetary theory in three dimensions with elliptic functions and elliptic integrals. In an earlier treatment, (Williams, Van Flandern, and Wright, 1987) presented a two dimensional planetary theory to the first order of a Picard iteration. The theory did avoid expansions in powers of the ratio of the semi-major axes and it contained only two explicit small divisors, n – n′ and 2n – n′. These advantages are retained in the new theory and in fact no small divisors appear explicitly. Secular terms are removed by adopting an averaging technique rather than continuing the Pica

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7

Kumano, Hironori, and Takanori Uka. "The Spatial Profile of Macaque MT Neurons Is Consistent With Gaussian Sampling of Logarithmically Coordinated Visual Representation." Journal of Neurophysiology 104, no. 1 (2010): 61–75. http://dx.doi.org/10.1152/jn.00040.2010.

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Neurons in extrastriate visual areas have large receptive fields (RFs) compared with those in primary visual cortex (V1), suggesting extensive spatial integration. To examine the spatial integration of neurons in area MT, we modeled the RFs of MT neurons based on a symmetrical (Gaussian) integration of V1 outputs and tested the model using single-unit recording in two fixating macaque monkeys. Because visual representation in V1 is logarithmically compressed along eccentricity, the resulting RF model is log-Gaussian along the radial axis in polar coordinates. To test the log-Gaussian model, th

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Jones, J. P., A. Stepnoski, and L. A. Palmer. "The two-dimensional spectral structure of simple receptive fields in cat striate cortex." Journal of Neurophysiology 58, no. 6 (1987): 1212–32. http://dx.doi.org/10.1152/jn.1987.58.6.1212.

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1. A quantitative, general purpose method was developed for measuring the responses of visual neurons to stimuli distributed with high resolution over the two-dimensional (2D) spatial frequency domain. The stimuli consisted of drifting sinusoidal gratings of nonsaturating contrasts whose spatial frequency and orientation were drawn in random order from a 16 X 16 array of coordinates covering each neuron's responsive area. This method was applied to a population of 36 simple cells in area 17 of cat. 2. The response of each simple cell to drifting sinusoidal gratings appeared as a rectified sinu

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9

Feng, W., M. P. Chipperfield, S. Davies, et al. "Three-dimensional model study of the Arctic ozone loss in 2002/2003 and comparison with 1999/2000 and 2003/2004." Atmospheric Chemistry and Physics 5, no. 1 (2005): 139–52. http://dx.doi.org/10.5194/acp-5-139-2005.

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Abstract. We have used the SLIMCAT 3-D off-line chemical transport model (CTM) to quantify the Arctic chemical ozone loss in the year 2002/2003 and compare it with similar calculations for the winters 1999/2000 and 2003/2004. Recent changes to the CTM have improved the model's ability to reproduce polar chemical and dynamical processes. The updated CTM uses σ-θ as a vertical coordinate which allows it to extend down to the surface. The CTM has a detailed stratospheric chemistry scheme and now includes a simple NAT-based denitrification scheme in the stratosphere. In the model runs presented he

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Feng, W., M. P. Chipperfield, S. Davies, et al. "Three-dimensional model study of the arctic ozone loss in 2002/2003 and comparison with 1999/2000 and 2003/2004." Atmospheric Chemistry and Physics Discussions 4, no. 5 (2004): 5045–74. http://dx.doi.org/10.5194/acpd-4-5045-2004.

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Abstract. We have used the SLIMCAT 3-D off-line chemical transport model (CTM) to quantify the Arctic chemical ozone loss in the year 2002/2003 and compare it with similar calculations for the winters 1999/2000 and 2003/2004. Recent changes to the CTM have improved the model's ability to reproduce polar chemical and dynamical processes. The updated CTM uses σ-θ as a vertical coordinate which allows it to extend down to the surface. The CTM has a detailed stratospheric chemistry scheme and now includes a simple NAT-based denitrification scheme in the stratosphere. In the model runs presented he

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András, Csaba Dezső, László Mátyás, Botond Ráduly, and Rozália Veronika Salamon. "Increasing the Prediction Efficiency of Hansen Solubility Parameters in Supercritical Fluids." Periodica Polytechnica Chemical Engineering 63, no. 2 (2019): 286–93. http://dx.doi.org/10.3311/ppch.12780.

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This work describes a simplified method developed for calculating the Hansen parameters (HSPs) for scCO2-polar modifier solvent mixtures. The method consists in fitting 2nd order equations on the calculated values of HSPs of pure components in function of pressure and temperature. It has been proved that these equations are suitable for the characterization of the above system. The current work also proposes a modified representation method, which eliminates the shortcomings of the original ternary Teas diagram, normally used for the representation of the Hansen parameters. On the one hand, th

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Jin, Xiaogang, and V. F. Li. "Three-Dimensional Deformation Using Directional Polar Coordinates." Journal of Graphics Tools 5, no. 2 (2000): 15–24. http://dx.doi.org/10.1080/10867651.2000.10487521.

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Leray, A., C. Spriet, D. Trinel, and Laurent HÃ©liot. "Three-dimensional polar representation for multispectral fluorescence lifetime imaging microscopy." Cytometry Part A 75A, no. 12 (2009): 1007–14. http://dx.doi.org/10.1002/cyto.a.20802.

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14

Chung, Won Sang. "The generalized uncertainty principle with commuting coordinates." Modern Physics Letters A 34, no. 33 (2019): 1950267. http://dx.doi.org/10.1142/s0217732319502675.

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In this paper, we present a new D-dimensional generalized uncertainty principle (GUP) algebra with commuting coordinates which recovers [Formula: see text] in one dimension. We find two representations for this GUP: momentum representation and position representation. We discuss the GUP-corrected three-dimensional quantum mechanics in position representation for a small [Formula: see text]. Finally, we discuss the momentum wave function and GUP-corrected Fermi metal theory.

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15

Baddour, Natalie. "Operational and convolution properties of three-dimensional Fourier transforms in spherical polar coordinates." Journal of the Optical Society of America A 27, no. 10 (2010): 2144. http://dx.doi.org/10.1364/josaa.27.002144.

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16

Zou, Shangyuan, Hairui Liu, Yanli Liu, Jiafeng Yao, and Hongtao Wu. "Singularity Analysis and Representation of 6DOF Parallel Robot Using Natural Coordinates." Journal of Robotics 2021 (June 10, 2021): 1–11. http://dx.doi.org/10.1155/2021/9935794.

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Singularity research is carried out. The problem, which is about six-dimensional parameters of position and orientation can not realize three-dimensional visualization for 6DOF parallel robot, has been solved. Firstly, according to the structural characteristics of the 6DOF parallel robot with the planar platform, the position and orientation of the mobile platform are described, respectively, and the six equations of forward kinematics are established by choosing the natural coordinates of three representative points as parameters. Then, the singularities of the 6DOF parallel robot with a pla

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Qi, Min, Xiao Xi Zhang, Da Jian Li, and Yang Yu Fan. "The Review of Algorithms to Correct Barrel Distortion Image." Advanced Materials Research 628 (December 2012): 403–9. http://dx.doi.org/10.4028/www.scientific.net/amr.628.403.

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Aiming at solving the problem of correcting barrel distortion of image, this paper concluded the common correction algorithms into three types which include Affine Transformation, Two Degree Polynomial Transformation and Polar Coordinate Transformation, and introduced the basic theory of each of their representative algorithm. Then, analyzed and compared the advantages and disadvantages of them according to the correction experiments. At last, pointed out the research directions and difficulties of this field. In conclusion, Polar Coordinate Transformation is the most appropriate method to cor

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Danielson, K. T., and A. K. Noor. "Finite Elements Developed in Cylindrical Coordinates for Three-Dimensional Tire Analysis." Tire Science and Technology 25, no. 1 (1997): 2–28. http://dx.doi.org/10.2346/1.2137529.

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Abstract Finite elements developed in cylindrical coordinates are presented for three-dimensional analysis of tires. In contrast to elements formulated in Cartesian coordinates, these elements allow the exact representation of circular shapes. The exact modeling of circular geometries can provide better finite element predictions and reduce the number of elements needed around the tire circumference. Numerical results are presented for the application of this formulation to the analysis of a radial automobile tire subjected to rim mounting, nonconservative inflation pressure, and rigid pavemen

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Apriandi, Davi, and Ika Krisdiana. "Analisis Kesulitan Mahasiswa dalam Memahami Materi Integral Lipat Dua pada Koordinat Polar Mata Kuliah Kalkulus Lanjut." Al-Jabar : Jurnal Pendidikan Matematika 7, no. 2 (2016): 123–34. http://dx.doi.org/10.24042/ajpm.v7i2.19.

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This study aims to determine the difficulties experienced by students in understanding the double integral in polar coordinates advanced calculus courses and the factors that cause these problems. This research is qualitative. Subjects were students of the fourth semester of academic year 2015/2016 Mathematics Education, IKIP PGRI Madiun totaling 3 persons. Data collection techniques have used that test, observation, interviews, and documentation. Data analysis technique conducted with qualitative data analysis, namely data reduction, data presentation and conclusion. The results were obtained

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Eapen, Naived George, Debabrata Samanta, Manjit Kaur, Jehad F. Al-Amri, and Mehedi Masud. "Elementary Methods for Generating Three-Dimensional Coordinate Estimation and Image Reconstruction from Series of Two-Dimensional Images." Mathematical Problems in Engineering 2021 (September 15, 2021): 1–11. http://dx.doi.org/10.1155/2021/9494368.

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The increase in computational power in recent years has opened a new door for image processing techniques. Three-dimensional object recognition, identification, pose estimation, and mapping are becoming popular. The need for real-world objects to be mapped into three-dimensional spatial representation is greatly increasing, especially considering the heap jump we obtained in the past decade in virtual reality and augmented reality. This paper discusses an algorithm to convert an array of captured images into estimated 3D coordinates of their external mappings. Elementary methods for generating

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McBain, G. D. "Plane poloidal-toroidal decomposition of doubly periodic vector fields. Part 1. Fields with divergence." ANZIAM Journal 47, no. 1 (2005): 21–38. http://dx.doi.org/10.1017/s1446181100009743.

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AbstractIt is shown how to decompose a three-dimensional field periodic in two Cartesian coordinates into five parts, three of which are identically divergence-free and the other two orthogonal to all divergence-free fields. The three divergence-free parts coincide with the mean, poloidal and toroidal fields of Schmitt and Wahl; the present work, therefore, extends their decomposition from divergence-free fields to fields of arbitrary divergence. For the representation of known and unknown fields, each of the five subspaces is characterised by both a projection and a scalar representation. Use

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Choi, Woong, Jongho Lee, and Liang Li. "Analysis of Three-Dimensional Circular Tracking Movements Based on Temporo-Spatial Parameters in Polar Coordinates." Applied Sciences 10, no. 2 (2020): 621. http://dx.doi.org/10.3390/app10020621.

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Motor control characteristics of the human visuomotor control system need to be analyzed in the three-dimensional (3D) space to study and imitate human movements. In this paper, we examined circular tracking movements on two planes in 3D space from a motor control perspective based on three temporospatial parameters in polar coordinates. Sixteen healthy human subjects participated in this study and performed circular target tracking movements rotating at 0.125, 0.25, 0.5, and 0.75 Hz in the frontal or sagittal planes in three-dimensional space. The results showed that two temporal parameter er

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Kaffka, Károly J., and László S. Gyarmati. "Investigating the Polar Qualification System." Journal of Near Infrared Spectroscopy 6, A (1998): A191—A200. http://dx.doi.org/10.1255/jnirs.193.

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A new, rapid qualification method was introduced at the 3rd International Conference on Near Infrared Spectroscopy according to which a “quality point” was defined on a two-dimensional “quality plane”. The quality point of the investigated material was given by the center of its spectrum represented in a polar coordinate system. The method was further developed, three interpretations were given for the “center” of the polar spectrum, resulting in three different formulas for determining the x and y coordinates of the quality point. The effect of the change in the amplitude of the absorption pe

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Teague, Richard, Marija R. Jankovic, Thomas J. Haworth, Chunhua Qi, and John D. Ilee. "A three-dimensional view of Gomez’s hamburger." Monthly Notices of the Royal Astronomical Society 495, no. 1 (2020): 451–59. http://dx.doi.org/10.1093/mnras/staa1167.

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ABSTRACT Unravelling the three-dimensional physical structure, the temperature and density distribution, of protoplanetary discs is an essential step if we are to confront simulations of embedded planets or dynamical instabilities. In this paper, we focus on submillimeter array observations of the edge-on source, Gomez’s Hamburger, believed to host an overdensity hypothesized to be a product of gravitational instability in the disc, GoHam b. We demonstrate that, by leveraging the well-characterized rotation of a Keplerian disc to deproject observations of molecular lines in position-position-v

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Ghaffari, Reza, and Roger A. Sauer. "A nonlinear thermomechanical formulation for anisotropic volume and surface continua." Mathematics and Mechanics of Solids 25, no. 11 (2020): 2076–117. http://dx.doi.org/10.1177/1081286520919483.

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A thermomechanical, polar continuum formulation under finite strains is proposed for anisotropic materials using a multiplicative decomposition of the deformation gradient. First, the kinematics and conservation laws for three-dimensional, polar, and nonpolar continua are obtained. Next, these kinematics and conservation laws are connected to their corresponding counterparts for surface continua, based on Kirchhoff–Love assumptions. Then the shell material models are extracted from three-dimensional material models for finite-temperature problems using established connections. The weak forms a

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Bourdarias, Christian, Stéphane Gerbi, and Jacques Ohayon. "A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates." ESAIM: Mathematical Modelling and Numerical Analysis 37, no. 4 (2003): 725–39. http://dx.doi.org/10.1051/m2an:2003044.

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Zakharov, Aleksey, and Arkady Zhiznyakov. "Synthesis of Three-Dimensional Models from Drawings Based on Spectral Graph Theory." Applied Mechanics and Materials 756 (April 2015): 598–603. http://dx.doi.org/10.4028/www.scientific.net/amm.756.598.

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Task of automatic reconstruction of three-dimensional objects by drawing views presented. The algorithm based on a boundary representation of three-dimensional models. The algorithm consists of the following steps: automatic separation of the drawing per the views, determination of three-dimensional coordinates of vertices, definition and marking of wire model primitives, reconstruction of model faces and model elements. The fundamental concept of the algorithm is to find the structural elements of three-dimensional model with usage of pre-specified patterns. The templates are described by mea

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Barr, Alan, and David Hawkins. "An Anatomical Database Providing Three-Dimensional Geometric Representation of Lower Limb Structures." Journal of Applied Biomechanics 16, no. 3 (2000): 301–8. http://dx.doi.org/10.1123/jab.16.3.301.

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An anatomical database was constructed containing three-dimensional geometric representations of the structures comprising the lower extremity. The database was constructed by digitizing 100 high-resolution digital photographic images supplied from the National Library of Medicine’s Visual Human Male (VHM) project. These images were taken of sequential transverse cross-sectional slices of the leg. Slices were located 1 cm apart between a location approximately 3 mm below the superior aspect of the ilium and approximately 2 mm below the distal end of the fibula. Image Tool Software (v. 2.0) was

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Bailey, David A., Amanda H. Lynch, and Katherine S. Hedström. "Impact of ocean circulation on regional polar climate simulations using the Arctic Region Climate System Model." Annals of Glaciology 25 (1997): 203–7. http://dx.doi.org/10.1017/s026030550001404x.

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Global climate models have pointed to the polar regions as very sensitive areas in response to climate change. However, these models often do not contain representations of processes peculiar to the polar regions such as dynamic sea ice, permafrost, and Arctic stratus clouds. Further, global models do not have the resolution necessary to model accurately many of the important processes and feedbacks. Thus, there is a need for regional climate models of higher resolution. Our such model (ARCSy M) has been developed by A. Lynch and W. Chapman. This model incorporates the NCAR Regional Climate Mo

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Bailey, David A., Amanda H. Lynch, and Katherine S. Hedström. "Impact of ocean circulation on regional polar climate simulations using the Arctic Region Climate System Model." Annals of Glaciology 25 (1997): 203–7. http://dx.doi.org/10.3189/s026030550001404x.

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Global climate models have pointed to the polar regions as very sensitive areas in response to climate change. However, these models often do not contain representations of processes peculiar to the polar regions such as dynamic sea ice, permafrost, and Arctic stratus clouds. Further, global models do not have the resolution necessary to model accurately many of the important processes and feedbacks. Thus, there is a need for regional climate models of higher resolution. Our such model (ARCSy M) has been developed by A. Lynch and W. Chapman. This model incorporates the NCAR Regional Climate Mo

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Olga Blazekova and Maria Vojtekova. "Using of Parallel Coordinates in Finding Minimum Distance in Time-Space." Communications - Scientific letters of the University of Zilina 21, no. 3 (2019): 3–7. http://dx.doi.org/10.26552/com.c.2019.3.3-7.

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Airspace domain may be represented by a time-space consisting of a three-dimensional Cartesian coordinate system and time as the fourth dimension. A coordinate system provides a scheme for locating points given its coordinates and vice versa. The choice of coordinate system is important, as it transforms data to geometric representation. Visualization of the three and more dimensional data on the two-dimensional drawing - computer monitor is usually done by projection, which often can restrict the amount of information presented at a time. Using the parallel coordinate system is one of possibi

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Chen, Fong-Zhi, Ming-June Tsai, Yu-Wen Chang, Rong-Yuan Jou, and Hong-Ping Cheng. "Using Plücker Coordinates for Pumping Speed Evaluation of Molecular Pump in the DSMC Method." International Journal of Rotating Machinery 7, no. 1 (2001): 11–20. http://dx.doi.org/10.1155/s1023621x01000021.

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In this study, the Plücker coordinates representation is used to formulate the ruled surface and the molecular path for pumping speed performance evaluation of a molecular vacuum pump. The ruled surface represented by the Pliicker coordinates is used to develop a criterion for when gas molecules hit the pump surface wall. The criterion is applied to analyze the flow rate of a new developed vacuum pump in transition regimes by using the DSMC (Direct Simulation Monte Carlo) method. When a molecule flies in a neutral electrical field its path is a straight line. If the molecular path and the gene

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Абдразакова, Анжела Романовна, and Антон Вацлавович Войтишек. "Computable simulated transformations of the Cartesian coordinates for random vectors." Вычислительные технологии, no. 6 (January 19, 2021): 62–84. http://dx.doi.org/10.25743/ict.2020.25.6.004.

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Рассмотрены специальные преобразования декартовых координат, позволяющие строить эффективные (экономичные) алгоритмы численного моделирования многомерных случайных величин. В качестве иллюстративных и практически значимых примеров таких преобразований рассмотрены переходы к полярным, сферическим, параболическим и цилиндрическим координатам. The purpose of the paper was to expand the range of efficient (economical) computer algorithms for simulation of multi-dimensional random variables. The authors noticed that in a number of applied problems (for example, when modelling twoor three-dimensiona

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Wang, Xiao Ling, and Hui Zhao. "Virtual Mechanical Equipment Model Smoothing." Advanced Materials Research 156-157 (October 2010): 355–59. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.355.

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We present a system to remove noise or smooth three dimensional (3D) virtual mechanical equipment models. Our system works not in well-known Euclidean space, but in Laplacian space [1, 2]. We transform the model from its global representation into the local representation. Then we manipulate the local property with the Laplacian Coordinates [1]. Our whole system can be modeled as a huge sparse linear system which can be solved very fast by state-of-art numerical solver [3].

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Vaina, Lucia, and Youcef Bennour. "A Computational Approach to Visual Recognition of Arm Movements." Perceptual and Motor Skills 60, no. 1 (1985): 203–28. http://dx.doi.org/10.2466/pms.1985.60.1.203.

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A representation for the visual recognition of skilled arm movements is proposed that lies within Mart and Vaina's (1982) three-dimensional model representation for shape movements. Algorithms for segmenting arm movements into pieces are proposed. It is suggested that for a large class of arm movements recognition could be reliably achieved based only on the description of the hand shape and path in the body coordinates, without needing the detailed description of the variation of all the joint angles of the arm.

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Qin, Fangjun, Lubin Chang, and An Li. "Improved Transversal Polar Navigation Mechanism for Strapdown INS using Ellipsoidal Earth Model." Journal of Navigation 71, no. 6 (2018): 1460–76. http://dx.doi.org/10.1017/s0373463318000425.

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As the geographical meridians converge rapidly, traditional inertial navigation methods fail in the polar regions. Classic transversal navigation methods can address the problem by transversal rotation of the original north and south poles, but this can introduce errors based on the spherical Earth model. To reduce the principle errors, some fruitful research work using an ellipsoidal Earth model has been done. Under the ellipsoid Earth model, transversal navigation for polar region becomes a complex coupling problem. Considering the coupling of the three-dimensional motion, a more rigorous me

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Guenther, Frank H., Daniel Bullock, Douglas Greve, and Stephen Grossberg. "Neural Representations for Sensorimotor Control. III. Learning a Body-Centered Representation of a Three-Dimensional Target Position." Journal of Cognitive Neuroscience 6, no. 4 (1994): 341–58. http://dx.doi.org/10.1162/jocn.1994.6.4.341.

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A neural model is described of how the brain may autonomously learn a body-centered representation of a three-dimensional (3-D) target position by combining information about retinal target position, eye position, and head position in real time. Such a body-centered spatial representation enables accurate movement commands to the limbs to be generated despite changes in the spatial relationships between the eyes, head, body, and limbs through time. The model learns a vector representation—otherwise known as a parcellated distributed representation—of target vergence with respect to the two eye

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Cooper, Martin, and John Sweller. "Secondary School Students' Representations of Solids." Journal for Research in Mathematics Education 20, no. 2 (1989): 202–12. http://dx.doi.org/10.5951/jresematheduc.20.2.0202.

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The study examined secondary school students' ability to interpret various representations of simple three-dimensional objects. Verbal descriptions, descriptions based on coordinates, graphical representations, and actual prototypes were employed. The two-dimensional graphical representations were plans, elevations, and perspective drawings. Grade 7, Grade 9, and Grade 11 students were given four identical wooden cubes and asked to construct the objects represented by a particular description, graphical representation, or prototype. For all ages studied, verbal descriptions, perspective drawin

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Krasheninnikov, V. R., O. E. Malenova, and A. U. Subbotin. "MODELS OF IMAGES WITH RADIAL-CIRCULAR STRUCTURE." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W12 (May 9, 2019): 123–27. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w12-123-2019.

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<p><strong>Abstract.</strong> The overwhelming majority of known image models are varieties of random fields defined on rectangular two-dimensional grids or grids of higher dimension, for example. In some practical situations, the images have an annular, radial or radial-circular structure. For example, images of the facies (thin film) of dried biological fluid, eyes, cut of a tree trunk or a fruit, blood vessel, erythrocyte, blast pattern, end face detail, etc. In addition, radar and other images are physically obtained in polar or spherical coordinates. These features of im

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Wang, Tong, and Zhang Kun Hu. "Simulation of Complex Curved Surface WEDM System Based on OpenGL." Applied Mechanics and Materials 10-12 (December 2007): 364–68. http://dx.doi.org/10.4028/www.scientific.net/amm.10-12.364.

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This paper introduces the characteristics and general laws of cutting complex curved surface by Wire-cut Electric Discharge Machining (WEDM) system. Taking the three-axle and double-rotating linkage system as an example, the universal mathematical model of polar coordinates is derived. Moreover, the simulation of WEDM system is introduced, which utilizing language Visual C++ and the three dimensional graph software OpenGL.This simulation method is helpful in improving machining quality and productivity of complex curved surfaces, and is fundation for establishing CAD/CAPP/CAM technology in WED

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Costa, K. D., P. J. Hunter, J. M. Rogers, J. M. Guccione, L. K. Waldman, and A. D. McCulloch. "A Three-Dimensional Finite Element Method for Large Elastic Deformations of Ventricular Myocardium: I—Cylindrical and Spherical Polar Coordinates." Journal of Biomechanical Engineering 118, no. 4 (1996): 452–63. http://dx.doi.org/10.1115/1.2796031.

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A three-dimensional Galerkin finite element method was developed for large deformations of ventricular myocardium and other incompressible, nonlinear elastic, anisotropic materials. Cylindrical and spherical elements were used to solve axisymmetric problems with r.m.s. errors typically less than 2 percent. Isochoric interpolation and pressure boundary constraint equations enhanced low-order curvilinear elements under special circumstances (69 percent savings in degrees of freedom, 78 percent savings in solution time for inflation of a thick-walled cylinder). Generalized tensor products of line

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Guangbao, Wang, and Ding Guangtao. "The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator." Advances in Mathematical Physics 2020 (August 1, 2020): 1–6. http://dx.doi.org/10.1155/2020/2378989.

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The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian funct

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Gopal, Venu, R. K. Mohanty, and Navnit Jha. "New Nonpolynomial Spline in Compression Method of for the Solution of 1D Wave Equation in Polar Coordinates." Advances in Numerical Analysis 2013 (September 30, 2013): 1–8. http://dx.doi.org/10.1155/2013/470480.

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We propose a three-level implicit nine point compact finite difference formulation of order two in time and four in space direction, based on nonpolynomial spline in compression approximation in -direction and finite difference approximation in -direction for the numerical solution of one-dimensional wave equation in polar coordinates. We describe the mathematical formulation procedure in detail and also discussed the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.

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Ziegler, Franz, and Piotr Borejko. "The Method of Generalized Ray-Revisited." Journal of Mechanics 16, no. 2 (2000): 125–26. http://dx.doi.org/10.1017/s1727719100001696.

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In Section 2, ROTATION OF COORDINATES, the Authors derived the emittance functions in the Weyl-Sommerfeld representation of the wave potentials for a horizontal instantaneous single force from those known for a vertical force from conditions of invariance of the phase and amplitude of plane waves under coordinate rotation, Eqs. (10) ∼ (13) and (18) ∼ (20). That transformation implies the validity of the commonly applied identity for the (force) vector components when rotating the vector in the opposite sense to the coordinate rotation. Further, in the three-dimensional case, the vertical force

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Piltner, R. "The representation of three-dimensional elastic displacement fields with the aid of complex valued functions for several curvilinear coordinates." Mechanics Research Communications 15, no. 2 (1988): 79–85. http://dx.doi.org/10.1016/0093-6413(88)90056-0.

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ROSENBAUM, MARCOS, ALEXANDER TURBINER, and ANTONIO CAPELLA. "SOLVABILITY OF THE G2 INTEGRABLE SYSTEM." International Journal of Modern Physics A 13, no. 22 (1998): 3885–903. http://dx.doi.org/10.1142/s0217751x98001815.

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It is shown that the three-body trigonometric G2 integrable system is exactly solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary values of the coupling constants, the Hamiltonian can be expressed as a quadratic polynomial in the generators of some Lie algebra of differential operators in a finite-dimensional representation. Four infinite families of eigenstates, represented by polynomials, and the corresponding eigenvalues are described explicitly.

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Pazderski, D., P. Szulczyński, and K. Kozłowski. "Closed-loop control algorithm for some class of nonholonomic systems using polar representation." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 3 (2012): 521–35. http://dx.doi.org/10.2478/v10175-012-0065-y.

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Abstract This paper is focused on the convergence problem defined for some class of a two input affine nonholonomic driftless system with three-dimensional state. The problem is solved based on a polar transformation which is singular at the origin. The convergence is ensured using static-state feedback. The necessary conditions for construction of the algorithm are formally discussed. The solution, in general, is local, and the feasible domain is strictly related to the properties of the control system. In order to improve algorithm robustness a simple hybrid algorithm is formulated. The gene

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Wang, Tong, K. Jiang, Shu Qiang Xie, and Shuang Shuang Hao. "Motion Analysis and Simulation of Complex Curved Surface WEDM System." Key Engineering Materials 392-394 (October 2008): 151–55. http://dx.doi.org/10.4028/www.scientific.net/kem.392-394.151.

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In this paper, the characteristics and general laws of cutting complex curved surface by wire electrical discharge machining (WEDM) system are studied. Based on analysis of motion parameters the universal mathematical model of polar coordinates is derived. Moreover, the simulation of WEDM system is introduced, which is carried out by using language Visual C++ and the three dimensional graph software OpenGL.This simulation method is helpful in improving machining quality and productivity of complex curved surfaces, and is fundation for establishing CAD/CAPP/CAM technology in WEDM.

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Zhang, Cheng Shan. "Analysis of Workspace for the 4-PUU Parallel Manipulator." Advanced Materials Research 542-543 (June 2012): 886–90. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.886.

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4-PUU parallel manipulator with three-dimensional translations and one rotational motion about Z axis was presented. The Workspace of boundary point was obtained by searching in Polar Coordinates,the workspace of standing pose was analyzed by programming with MATLAB and LabVIEW. The research indicated that the workspace of the 4-PUU parallel mechanism has advantages of smooth boundary, big volume, no cavity and regular cross section in the fields of industrial robots, micromanipulators, virtual axis machine tools, damping platform, rehabilitation robot and etc.

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Stephenson, R. W., and K. E. Rouch. "Modeling Rotating Shafts Using Axisymmetric Solid Finite Elements with Matrix Reduction." Journal of Vibration and Acoustics 115, no. 4 (1993): 484–89. http://dx.doi.org/10.1115/1.2930376.

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An axisymmetric harmonic finite element representation is used to calculate shaft lateral critical speeds and perform stability analysis. Unlike a beam element model, an axisymmetric solid element representation allows the actual rotor geometry to be modeled. A Fourier series representation allows the three-dimensional shaft geometry to be modeled in two dimensions by only considering the radial and axial coordinates. Thus, the degrees of freedom of this element type are different from the usual two translations and two rotations at each node associated with bending of a three-dimensional beam

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