Results 71 to 80 of about 12,663 (185)
A Characterization of the Angle Defect and the Euler Characteristic in Dimension 2 [PDF]
Discrete & Computational Geometry, 2008 The ``Descartes-Gauss-Bonnet Theorem'' \(\sum_{v\in M} d(v,M) = 2\pi \chi(M)\) relates the curvature (angle defect or deficiency) \(d(v,M):=2\pi - \sum_{\alpha\ni v} \alpha\) at the vertices \(v\) of a triangulated polyhedral surface \(M\) to the Euler characteristic \(\chi(M)\) of \(M\).
openaire +1 more source
Shuttle Program. Euler angles, quaternions, and transformation matrices working relationships
, 1977 A brief mathematical development of the relationship between the Euler angles and the transformation matrix, the quaternion and the transformation matrix, and the Euler angles and the quaternion is presented.
Henderson, D. M.
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Euler angles, quaternions, and transformation matrices for space shuttle analysis
, 1977 Relationships between the Euler angles and the transformation matrix, the quaternion and the transformation matrix, and the Euler angles and the quaternion are analyzed, and equations developed are applied directly to current space shuttle problems.
Henderson, D. M.
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Globographic visualisation of three dimensional joint angles
Three different methods for describing three dimensional joint angles are commonly used in biomechanics. The joint coordinate system and Cardan/Euler angles are conceptually quite different but are known to represent the same underlying mathematics. More
Baker, RJ
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Orientlib: An R Package for Orientation Data
Journal of Statistical Software, 2003 Orientlib is an R package to facilitate working with orientation data, i.e. elements of S O(3). It provides automatic translation between different representations of orientations, including rotation matrices, quaternions, Euler angles and skew-symmetric
Duncan Murdoch
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Application of quaternion in visual simulation of rigid body motion
Journal of Measurement Science and Instrumentation, 2017 In recent years,with the extensive applications of high performance computer and the rapid development of the attitude control of the spacecraft,quaternion theory has been widely used.Compared with Euler angles,quaternion not only is simple calculation ...
HUANG Jin-yang +3 more
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, 2018 Based on Kirchhoff theory, governing equations of a spatial curved beam with an arbitrary undeformed configuration that undergoes large deformation are established in an arc-length coordinate system and axial extension of the beam is considered. Modified
Zhu, Weidong +3 more
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Wannier states in Euler angles coordinate basis
, 2001 This work is devoted to calculate the doubly excited states in the two-electron atom. The electrons in two-electron atom are described by three inner coordinates and by three Euler angles giving rotation of the system as a whole.
Nikitin S. I., Abdelhay S. M.
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Advanced quaternion forward kinematics algorithm including overview of different methods for robot kinematics [PDF]
FME Transactions, 2014 Formulation of proper and efficient algorithms for robot kinematics is essential for the analysis and design of serial manipulators. Kinematic modeling of manipulators is most often performed in Cartesian space.
Vidaković Jelena Z. +4 more
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A Universal Formula for Extracting the Euler Angles
, 2004 Recently, the authors completed a study of the Davenport angles, which are a generalization of the Euler angles for which the initial and final Euler axes need not be either mutually parallel or mutually perpendicular or even along the coordinate axes ...
Markley, F. Landis, Shuster, Malcolm D.
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