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Journal articles on the topic 'Angles of Euler'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Wren, Tishya A. L., and Paul C. Mitiguy. "A Simple Method to Obtain Consistent and Clinically Meaningful Pelvic Angles from Euler Angles during Gait Analysis." Journal of Applied Biomechanics 23, no. 3 (2007): 218–23. http://dx.doi.org/10.1123/jab.23.3.218.

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Clinical gait analysis usually describes joint kinematics using Euler angles, which depend on the sequence of rotation. Studies have shown that pelvic obliquity angles from the traditional tilt-obliquity-rotation (TOR) Euler angle sequence can deviate considerably from clinical expectations and have suggested that a rotation-obliquity-tilt (ROT) Euler angle sequence be used instead. We propose a simple alternate approach in which clinical joint angles are defined and exactly calculated in terms of Euler angles from any rotation sequence. Equations were derived to calculate clinical pelvic elev

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2

Jouybari, A., A. A. Ardalan, and M. H. Rezvani. "EXPERIMENTAL COMPARISON BETWEEN MAHONEY AND COMPLEMENTARY SENSOR FUSION ALGORITHM FOR ATTITUDE DETERMINATION BY RAW SENSOR DATA OF XSENS IMU ON BUOY." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W4 (September 27, 2017): 497–502. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w4-497-2017.

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The accurate measurement of platform orientation plays a critical role in a range of applications including marine, aerospace, robotics, navigation, human motion analysis, and machine interaction. We used Mahoney filter, Complementary filter and Xsens Kalman filter for achieving Euler angle of a dynamic platform by integration of gyroscope, accelerometer, and magnetometer measurements. The field test has been performed in Kish Island using an IMU sensor (Xsens MTi-G-700) that installed onboard a buoy so as to provide raw data of gyroscopes, accelerometers, magnetometer measurements about 25 mi

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3

Liu, Wu, Qiu Li, Gang Jin, and Wei Qiu. "Measurement of the Euler Angles of Wurtzitic ZnO by Raman Spectroscopy." Journal of Spectroscopy 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/6430540.

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A Raman spectroscopy-based step-by-step measuring method of Euler angles φ,θ,and ψ was presented for the wurtzitic crystal orientation on a microscopic scale. Based on the polarization selection rule and coordinate transformation theory, a series of analytic expressions for the Euler angle measurement using Raman spectroscopy were derived. Specific experimental measurement processes were presented, and the measurement of Raman tensor elements and Euler angles of the ZnO crystal were implemented. It is deduced that there is a trigonometric functional relationship between the intensity of each R

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4

Cacciatori, Sergio L., Bianca L. Cerchiai, Alberto Della Vedova, Giovanni Ortenzi, and Antonio Scotti. "Euler angles for G2." Journal of Mathematical Physics 46, no. 8 (2005): 083512. http://dx.doi.org/10.1063/1.1993549.

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5

Shuster, Malcolm D., and F. Landis Markley. "Generalization of the Euler Angles." Journal of the Astronautical Sciences 51, no. 2 (2003): 123–32. http://dx.doi.org/10.1007/bf03546304.

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6

Rathod, Cheta, and Ahmed A. Shabana. "Rail Geometry and Euler Angles." Journal of Computational and Nonlinear Dynamics 1, no. 3 (2006): 264–68. http://dx.doi.org/10.1115/1.2198878.

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In railroad vehicle dynamics, Euler angles are often used to describe the track geometry (track centerline and rail space curves). The tangent and curvature vectors as well as local geometric properties such as the curvature and torsion can be expressed in terms of Euler angles. Some of the local geometric properties and Euler angles can be related to measured parameters that are often used to define the track geometry. The Euler angles employed, however, define a coordinate system that may differ from the Frenet frame used in the classical differential geometry. The relationship between the t

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7

Nolze, Gert. "Euler angles and crystal symmetry." Crystal Research and Technology 50, no. 2 (2015): 188–201. http://dx.doi.org/10.1002/crat.201400427.

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8

Wu, Bin, Peng Chen, Yong Jiang Hu, and Chang Long Wang. "Research on Attitude Singularity Problem of Small Tail-Sitter Aircraft." Applied Mechanics and Materials 599-601 (August 2014): 401–4. http://dx.doi.org/10.4028/www.scientific.net/amm.599-601.401.

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Singularity problem in attitude estimation of small tail-sitter aircraft with traditional algorithm is researched. According to the flight characteristics of small tail-sitter aircraft, a new algorithm is proposed. Vertical Euler angles whose singularity points are away from standard Euler angles are introduced. Only one set of angles are used in horizontal or near-vertical state to avoid singularity. Simulation results show that attitude angles can vary continuously and have high accuracy under the condition of a large tilting angle.

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9

Milligan, T. "More applications of Euler rotation angles." IEEE Antennas and Propagation Magazine 41, no. 4 (1999): 78–83. http://dx.doi.org/10.1109/74.789738.

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10

Ying, Ning, and Wangdo Kim. "Determining Dual Euler Angles of the Ankle Complex in vivo Using “Flock of Birds” Electromagnetic Tracking Device." Journal of Biomechanical Engineering 127, no. 1 (2005): 98–107. http://dx.doi.org/10.1115/1.1846072.

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The dual Euler angles method has been proposed as an alternative approach to describe the general spatial human joint motion. In this study, the dual Euler angles method was applied to study the three-dimensional motion of the ankle complex. The methodology for obtaining dual Euler angles of the ankle complex was developed by using a “Flock of Birds” electromagnetic tracking device. The repeatability of the methodology was studied based on the intertester and intratester variability analysis. Finally kinematic coupling characteristics of the ankle complex during dorsiflexion–plantarflexion, ev

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11

Han, Songlai, and Jinling Wang. "A Novel Method to Integrate IMU and Magnetometers in Attitude and Heading Reference Systems." Journal of Navigation 64, no. 4 (2011): 727–38. http://dx.doi.org/10.1017/s0373463311000233.

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Modern attitude and heading reference systems (AHRS) generally use Kalman filters to integrate gyros with some other augmenting sensors, such as accelerometers and magnetometers, to provide a long term stable orientation solution. The construction of the Kalman filter for the AHRS is flexible, while the general options are the methods based on quaternion, Euler angles, or Euler angle errors. But the quaternion and Euler angle based methods need to model system angular motions, and, meanwhile, all these three methods suffer from nonlinear problems which will increase the system complexities and

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12

Dong, Yi Qun, Li Dong Zhang, Yi Jun Zhang, and Jian Liang Ai. "Attitude Protection Control for Side Stick-Operated Aircraft." Advanced Materials Research 846-847 (November 2013): 77–85. http://dx.doi.org/10.4028/www.scientific.net/amr.846-847.77.

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A control framework to limit aircraft Euler angles (pitch/rolling) under adverse side stick command adding is introduced. Attitude envelope of the aircraft pitch/rolling angle is discussed based on geometrical position of the aircraft relative to the ground. Control law of is established by using linearized predictive control strategy. The simulation test presents the performance of attitude protection restricting the Euler angles within the required envelop at 1,000m. Based on the test work discussed herein, the control work proposed in this paper is believed to be applicable.

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13

Brezov, Danail S., Clementina D. Mladenova, and Ivaïlo M. Mladenov. "Generalized Euler Angles Viewed as Spherical Coordinates." Geometry, Integrability and Quantization 18 (2017): 105–16. http://dx.doi.org/10.7546/giq-18-2017-105-116.

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14

Bertini, Stefano, Sergio L. Cacciatori, and Bianca L. Cerchiai. "On the Euler angles for SU(N)." Journal of Mathematical Physics 47, no. 4 (2006): 043510. http://dx.doi.org/10.1063/1.2190898.

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15

Menon, V. J. "On the Euler angles for infinitesimal rotations." European Journal of Physics 21, no. 1 (2000): 91–93. http://dx.doi.org/10.1088/0143-0807/21/1/313.

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16

Dattoli, G., E. Sabia, and A. Torre. "CKM matrix exponential parametrization and Euler angles." Il Nuovo Cimento A 110, no. 5 (1997): 487–96. http://dx.doi.org/10.1007/bf03035895.

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17

Pai, P. Frank. "Geometrically exact beam theory without Euler angles." International Journal of Solids and Structures 48, no. 21 (2011): 3075–90. http://dx.doi.org/10.1016/j.ijsolstr.2011.07.003.

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18

Shuster, Malcolm D., and F. Landis Markley. "General Formula for Extracting the Euler Angles." Journal of Guidance, Control, and Dynamics 29, no. 1 (2006): 215–21. http://dx.doi.org/10.2514/1.16622.

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19

Barbaraci, Gabriele. "Modeling and control of a quadrotor with variable geometry arms." Journal of Unmanned Vehicle Systems 3, no. 2 (2015): 35–57. http://dx.doi.org/10.1139/juvs-2014-0012.

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The goal of this paper is to study the dynamics of a quadcopter using a variable geometry structure and discuss the advantages of using the geometry variation. A mathematical model has been described using simulation to show quadcopter dynamics. Based on the different geometric configurations of arms it is shown how the arms’ angles affect longitudinal and lateral dynamics. The design's assumptions refer to hovering and rotation with Euler angles. Simulation results show that both controllers stabilize the quadrotor and the amplitude of the vibrations is significantly decreased, compared to th

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20

Perrusquía, Adolfo, and Wen Yu. "Human-in-the-Loop Control Using Euler Angles." Journal of Intelligent & Robotic Systems 97, no. 2 (2019): 271–85. http://dx.doi.org/10.1007/s10846-019-01058-2.

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21

Onaka, Susumu, and Kunio Hayashi. "Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix." Scanning 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/4893956.

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The logarithmln⁡Rof rotation matrixRis a skew symmetric tensor consisting of three independent elements of real numbers. In addition to the Euler angles and the axis/angle pair, the elements ofln⁡Rcalled the log angles are also the set of three parameters ofR. In this paper, we will show that the concept of the log angles is also useful to discuss changes in crystal orientations. The changes inRas a function of the position are given by the changes in the log angles. As an example, orientation changes caused by arrays of dislocations in a plastically deformed Cu single crystal are discussed.

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22

Siminovitch, David J. "A Classical View of the Euler Angles and the Euler Kinematic Equations in NMR." Journal of Magnetic Resonance, Series A 117, no. 2 (1995): 235–45. http://dx.doi.org/10.1006/jmra.1995.0767.

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23

Ozgoren, M. Kemal. "Comparative study of attitude control methods based on Euler angles, quaternions, angle–axis pairs and orientation matrices." Transactions of the Institute of Measurement and Control 41, no. 5 (2018): 1189–206. http://dx.doi.org/10.1177/0142331218773519.

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This paper presents a comparative study about the attitude control methods based on four commonly used error indicators, namely the triad of 3-2-1 deviational Euler angles, the error quaternion, the deviational angle–axis pair and the orientation error matrix. These error indicators are used here with the same backstepping control law to have a common basis of comparison. This control law makes the controller track a restoring angular velocity generated here specifically for each error indicator. This comparative study shows that all these error indicators can be used satisfactorily even in th

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24

Hu, Xing Zhi, Xiao Qian Chen, and Yong Zhao. "Coordinate Transform Methods Used in Dynamic Simulation of Satellite Separation." Advanced Materials Research 569 (September 2012): 712–17. http://dx.doi.org/10.4028/www.scientific.net/amr.569.712.

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Direction cosine matrix, Euler angles and quaternions are the common methods for translating vector equations into scalar equations. These methods used in separation simulation lack systematic discussion and comparison. This article is trying to present a proper coordinate transformation method for dynamic analysis of satellite separation. 321 and 123 rotations of Euler angles are proposed to construct the dynamic equations, which is different from simulation of missiles by the rotation of 321 and 231. Both Euler angles and quaternions are adopted to model the separation process of a small sat

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25

Burger, H. A. "Use of Euler-rotation angles for generating antenna patterns." IEEE Antennas and Propagation Magazine 37, no. 2 (1995): 56–63. http://dx.doi.org/10.1109/74.382344.

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26

Millot, Yannick, and Pascal P. Man. "Active and passive rotations with Euler angles in NMR." Concepts in Magnetic Resonance Part A 40A, no. 5 (2012): 215–52. http://dx.doi.org/10.1002/cmr.a.21242.

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27

Furlan, P. "Generalized Euler angles as intrinsic coordinates for nonlinear spinors." Journal of Mathematical Physics 28, no. 6 (1987): 1223–30. http://dx.doi.org/10.1063/1.527522.

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28

Hirsch, Steven M., Devon Frayne, Stephen Brown, and David M. Frost. "Interpreting Knee Valgus: Orthogonal Distance Vs Cardan/Euler Angles." Medicine & Science in Sports & Exercise 52, no. 7S (2020): 255–56. http://dx.doi.org/10.1249/01.mss.0000676340.24399.24.

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29

FIGAT, Marcin, and Zdobysław GORAJ. "ANALYSIS OF STABILITY DERIVATIVES IMPORTANT TO RECOVERY FROM SPIN." Aviation 20, no. 2 (2016): 48–52. http://dx.doi.org/10.3846/16487788.2016.1195060.

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This paper describes the numerical analysis of light aircraft stability derivatives in a wide range of angles of attack, important for recovery from spin. Stability derivatives versus angle of attack and sideslip were calculated using a CFD software, based on Euler equation combined with boundary layer equations. The analysis was performed up to the 40 deg of angle of attack and up to 25 deg of sideslip.

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30

LaScalza, Suzanne, Linda N. Gallo, James E. Carpenter, and Richard E. Hughes. "A Method for Measuring Euler Rotation Angles and Helical Axis of Upper Arm Motion." Journal of Applied Biomechanics 18, no. 4 (2002): 374–83. http://dx.doi.org/10.1123/jab.18.4.374.

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Clinical observation suggests that shoulder pathologies such as rotator cuff disorders and shoulder instability may alter the normal shoulder rhythm or relative motions of the structures comprising the shoulder girdle. The purpose of this study was to assess the accuracy of using a skin-mounted humeral cuff that could be used in vivo to determine Euler rotation angles and the helical axis of motion (HAM) during upper extremity movements. An in vitro model was used to compare the kinematics determined from the externally applied humeral cuff to the kinematics measured directly from the humerus.

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31

Zhang, Hongmei, Huaqing Zhang, Guangyan Xu, Hao Liu, and Xin Liu. "Attitude anti-interference federal filtering algorithm for MEMS-SINS/GPS/magnetometer/SV integrated navigation system." Measurement and Control 53, no. 1-2 (2020): 46–60. http://dx.doi.org/10.1177/0020294019882965.

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The attitude measurement systems composed of magnetic, angular rate and gravity sensors in the navigation system of an unmanned aerial vehicle are vulnerable to disturbed magnetic field observations. In this paper, an anti-interference integrated navigation federal Kalman filter is designed with fusing the information of microelectromechanical-system-based strapdown inertial navigation system, gravity field, geomagnetic field and solar vector (direction of sun). The filter works in the mode of fusion reset or no reset according to environmental conditions or manual setting. In addition, the ch

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32

Oh, Sung, Lee, Lee, Lee, and Yu. "Accurate Measurement Calculation Method for Interferometric Radar Altimeter-Based Terrain Referenced Navigation." Sensors 19, no. 7 (2019): 1688. http://dx.doi.org/10.3390/s19071688.

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In order to improve the performance of Terrain Referenced Navigation (TRN), an Interferometric Radar Altimeter (IRA) has been developed as a more accurate altimeter. The IRA outputs not only the relative distance (slant range, R) but also the cross-track angle (look angle, θ) of the closest point on the zero Doppler line by using the principle of interferometry and two or more antennas. To perform TRN using the IRA, the 3D relative position of the closest point should be calculated. There is a formula to calculate the relative position of the closest point using the Euler angles. However, in a

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33

Morawiec, A., and J. Pospiech. "Some Information on Quaternions Useful in Texture Calculations." Textures and Microstructures 10, no. 3 (1989): 211–16. http://dx.doi.org/10.1155/tsm.10.211.

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Crystal orientation is described by a rotation which can be expressed by a great number of different sets of parameters. Among these, the quaternion representation is the most economic one. The basic properties of quaternions are briefly summarized and their interrelationships with other orientation coordinates such as rotation axis and angle, the orientation matrix, and the Euler angles are given.

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34

Ioannidou, Stefania, and George Pantazis. "Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra." ISPRS International Journal of Geo-Information 9, no. 9 (2020): 494. http://dx.doi.org/10.3390/ijgi9090494.

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The three-dimensional coordinate’s transformation from one system to another, and more specifically, the Helmert transformation problem, is one of the most well-known transformations in the field of engineering. In this paper, its solution, in reverse problem, was investigated for specific data using three different methods. It is presented by solving it with the method of Euler angles as well as with the use of quaternion and dual-quaternion algebra, after first giving some basic mathematical theory. After research, not only were three artificial sets of data used, which were structured in a

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35

Piovan, Giulia, and Francesco Bullo. "On Coordinate-Free Rotation Decomposition: Euler Angles About Arbitrary Axes." IEEE Transactions on Robotics 28, no. 3 (2012): 728–33. http://dx.doi.org/10.1109/tro.2012.2184951.

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36

Tilma, Todd, Mark Byrd, and E. C. G. Sudarshan. "A parametrization of bipartite systems based onSU(4) Euler angles." Journal of Physics A: Mathematical and General 35, no. 48 (2002): 10445–65. http://dx.doi.org/10.1088/0305-4470/35/48/315.

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37

Lesk†, Arthur M. "On the calculation of Euler angles from a rotation matrix." International Journal of Mathematical Education in Science and Technology 17, no. 3 (1986): 335–37. http://dx.doi.org/10.1080/0020739860170309.

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38

D'Alessandro, Domenico. "Optimal evaluation of generalized Euler angles with applications to control." Automatica 40, no. 11 (2004): 1997–2002. http://dx.doi.org/10.1016/j.automatica.2004.06.006.

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39

Ling, Hao, and Ahmed A. Shabana. "Euler angles and numerical representation of the railroad track geometry." Acta Mechanica 232, no. 8 (2021): 3121–39. http://dx.doi.org/10.1007/s00707-020-02903-4.

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40

Ko, Nak, Seokki Jeong, Suk-seung Hwang, and Jae-Young Pyun. "Attitude Estimation of Underwater Vehicles Using Field Measurements and Bias Compensation." Sensors 19, no. 2 (2019): 330. http://dx.doi.org/10.3390/s19020330.

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This paper proposes a method of estimating the attitude of an underwater vehicle. The proposed method uses two field measurements, namely, a gravitational field and a magnetic field represented in terms of vectors in three-dimensional space. In many existing methods that convert the measured field vectors into Euler angles, the yaw accuracy is affected by the uncertainty of the gravitational measurement and by the uncertainty of the magnetic field measurement. Additionally, previous methods have used the magnetic field measurement under the assumption that the magnetic field has only a horizon

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41

Caccavale, Fabrizio, Ciro Natale, Bruno Siciliano, and Luigi Villani. "Resolved-acceleration control of robot manipulators: A critical review with experiments." Robotica 16, no. 5 (1998): 565–73. http://dx.doi.org/10.1017/s0263574798000290.

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The goal of this paper is to provide a critical review of the well-known resolved-acceleration technique for the tracking control problem of robot manipulators in the task space. Various control schemes are surveyed and classified according to the type of end-effector orientation error; namely, those based on Euler angles feedback, quaternion feedback, and angle/axis feedback. In addition to the assessed schemes in the literature, an alternative Euler angles feedback scheme is proposed which shows an advantage in terms of avoidance of representation singularities. An insight into the features

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42

Zheng, Li Li, and Yu Xian Jiang. "A Single CCD Algorithm to Determine the Position and Attitude during Rolling Phase of Rendezvous and Docking." Applied Mechanics and Materials 190-191 (July 2012): 813–18. http://dx.doi.org/10.4028/www.scientific.net/amm.190-191.813.

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Propose a new algorithm that use Euler angles to calculate directly large relative position and attitude of rendezvous and docking. By analyzing the feasibility of using Euler angles to solve instead of using quaternion and deriving the relations between the coordinates of the identification-points and the coordinates of point-images, a group of non-linear equations including relative position and attitude is established. It is proved that three non-collinear points are sufficient and required to determine the position and attitude uniquely. The whole deriving process does not mention any assu

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43

Wang, Song Shan, and Yan Qing Qi. "A Virtual Human's Driving Method Based on Motion Capture Data." Advanced Materials Research 711 (June 2013): 500–505. http://dx.doi.org/10.4028/www.scientific.net/amr.711.500.

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This article gives a method about driving a virtual human by motion capture data in software Jack. Firstly simplify Jack's skeleton model according to the skeleton of capturing data BVH. Secondly set up an Euler angle rotation equation to mapping joint angles between BVH and Jack. Finally, program the method and give an example to show that it is available to improve Jacks human motion simulating by the human capturing data.

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44

Jansen, J. F., R. L. Kress, and S. M. Babcock. "Controller Design for a Force-Reflecting Teleoperator System With Kinematically Dissimilar Master and Slave." Journal of Dynamic Systems, Measurement, and Control 114, no. 4 (1992): 641–49. http://dx.doi.org/10.1115/1.2897736.

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The purpose of this paper is to develop a controller for a force-reflecting teleoperator system having kinematically dissimilar master and slave. The controller is a stiffness controller for both the master and the slave. A mathematical problem associated with representing orientations using Euler angles is described, and Euler parameters are proposed as a solution. The basic properties of Euler parameters are presented, specifically those pertaining to stiffness control. The stiffness controller for both the master and the slave is formulated using Euler parameters to represent orientation an

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45

Rimrott, F. P. J., W. M. Szczygielski, and B. Tabarrok. "Kinetic Energy and Complementary Kinetic Energy in Gyrodynamics." Journal of Applied Mechanics 60, no. 2 (1993): 398–405. http://dx.doi.org/10.1115/1.2900807.

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The concepts of kinetic energy and complementary kinetic energy permit to distinguish between two different formulations of what happens to be the same quantity in Newtonian mechanics. These formulations turn out to play a significant role in gyrodynamics in that they can be used very effectively to establish fundamental equations. It is relatively straightforward to establish a complementary kinetic energy expression. The establishment of the kinetic energy expression is, in spite of its unambiguous definition, more complicated, and a way is presented how to obtain it without too much difficu

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46

Imhof, Janos. "Orientation Analysis." Materials Science Forum 1016 (January 2021): 605–10. http://dx.doi.org/10.4028/www.scientific.net/msf.1016.605.

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Simple figures illustrate the basic concepts: orientation, Euler angles, Euler space, orientation density function, pole density function. The iteration that decisively influenced the development of orientation analysis follows directly from the relationship between the two density functions. The minimum principle defines the initial function and the structure of the iteration. Using model orientation density function, we prove that this kind of orientation analysis is extremely effective.

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47

Feuerbacher, M. "Moiré, Euler and self-similarity – the lattice parameters of twisted hexagonal crystals." Acta Crystallographica Section A Foundations and Advances 77, no. 5 (2021): 460–71. http://dx.doi.org/10.1107/s2053273321007245.

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A real-space approach for the calculation of the moiré lattice parameters for superstructures formed by a set of rotated hexagonal 2D crystals such as graphene or transition-metal dichalcogenides is presented. Apparent moiré lattices continuously form for all rotation angles, and their lattice parameter to a good approximation follows a hyperbolical angle dependence. Moiré crystals, i.e. moiré lattices decorated with a basis, require more crucial assessment of the commensurabilities and lead to discrete solutions and a non-continuous angle dependence of the moiré-crystal lattice parameter. In

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48

HUAI, Chuangfeng. "USING EULER ANGLES TO EXPRESS MECHANICAL MODEL OF WALKING ROBOT SYSTEM." Chinese Journal of Mechanical Engineering 42, supp (2006): 48. http://dx.doi.org/10.3901/jme.2006.supp.048.

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49

Bernstein, Dennis S. "On Feasible Body, Aerodynamic, and Navigation Euler Angles for Aircraft Flight." Journal of Guidance, Control, and Dynamics 42, no. 5 (2019): 1130–35. http://dx.doi.org/10.2514/1.g003930.

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50

ZHOU JIN-YUAN, LI LI-YUN, and YE CHAO-HUI. "NUMERICAL CALCULATION TO THE EULER ANGLES FOR A SHAPED SELECTIVE PULSE." Acta Physica Sinica 45, no. 7 (1996): 1107. http://dx.doi.org/10.7498/aps.45.1107.

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