Results 231 to 240 of about 104,411 (281)
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Relativistic spin and Euler angles
Annals of Physics, 1966Abstract The Bargmann-Wigner equations for particles of mass m ≠ 0 and spin s ≠ 0 are derived from a set of equations involving differential operators only. To this aim, an expansion of the wave function with respect to a suitable set of functions of Euler angles is utilized.
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Performing Euler angle rotations in cad systems
Computer-Aided Design, 1995The elementary result of this note can be extended and proved as follows. Let \(A\), \(B\) be the matrix representations of two linear transformations acting on a space \(V\) relative to a frame \(e\). Then the representation of the map of \(B\) in the frame \(Ae\) is \(B'= A^{-1} BA\). Hence, \(AB'= BA\). By induction, let \(A_ i'= (A_ 1\cdots A_{i-1})
Lee, Y. T., Koh, A. S.
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Euler Angles, Bryant Angles and Euler Parameters
2015This chapter deals with the different approaches for describing the rotational coordinates in spatial multibody systems. In this process, Euler angles and Bryant angles are briefly characterized. Particular emphasis is given to Euler parameters, which are utilized to describe the rotational coordinates in the present work.
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IEEE Transactions on Automatic Control, 1966
The definition of sets of Euler angles is discussed and a useful tool for treating the mathematics associated with Euler angles is illustrated. Restricting attention to right-handed coordinate systems and positive rotations, twelve distinct but equivalent sets of Euler angles are partitioned into two subsets.
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The definition of sets of Euler angles is discussed and a useful tool for treating the mathematics associated with Euler angles is illustrated. Restricting attention to right-handed coordinate systems and positive rotations, twelve distinct but equivalent sets of Euler angles are partitioned into two subsets.
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2012
As frequently noted in the literature on robotics (Sugihara et al. 2002; Kurazume et al. 2003; Vukobratovic et al. 2007; Kwon and Park 2009) and mechanisms (Duffy 1978; Chaudhary and Saha 2007), a higher Degrees-of-Freedom (DOF) joint, say, a universal, a cylindrical or a spherical joint, can be represented using a combination of several intersecting 1-
Suril Vijaykumar Shah +2 more
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As frequently noted in the literature on robotics (Sugihara et al. 2002; Kurazume et al. 2003; Vukobratovic et al. 2007; Kwon and Park 2009) and mechanisms (Duffy 1978; Chaudhary and Saha 2007), a higher Degrees-of-Freedom (DOF) joint, say, a universal, a cylindrical or a spherical joint, can be represented using a combination of several intersecting 1-
Suril Vijaykumar Shah +2 more
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Error analysis of Euler angle transformations
Guidance and Control Conference, 1972Error analyses of Euler angle transformations arise in the design of precision pointing systems, guidance systems and other systems containing gimbals. The generalized problem, including nonorthogonality of nominally orthogonal coordinate axes as well as errors in the Euler angles, is treated.
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How to Draw Euler Angles and Utilize Euler Parameters
Volume 2: 30th Annual Mechanisms and Robotics Conference, Parts A and B, 2006This article presents a way to draw Euler angles such that the proper operation and application becomes immediately clear. Furthermore, Euler parameters, which allow a singularity-free description of rotational motion, are discussed within the frame-work of quaternion algebra and are applied to the kinematics and dynamics of a rigid body.
A. L. Schwab, J. P. Meijaard
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Euler's parallel oblique-angled diameters
The Mathematical Gazette, 2011In the paper [1], Euler was examining properties of the conic sections that could be shared by more general curves. Most of the paper is concerned with ‘oblique-angle diameters’, a concept that seems to have been familiar to his readers in the eighteenth century, but has been ignored today.
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Denavit-Hartenberg Parameterization of Euler Angles
Journal of Computational and Nonlinear Dynamics, 2012Euler angles describe rotations of a rigid body in three-dimensional Cartesian space, as can be obtained by, say, a spherical joint. The rotation carried out by a spherical joint can also be expressed by using three intersecting revolute joints that can be described using the popular Denavit-Hartenberg (DH) parameters.
S. V. Shah, S. K. Saha, J. K. Dutt
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Euler angles and crystal symmetry
Crystal Research and Technology, 2015For the description of (single) crystal orientations, e.g. as measured by electron backscatter diffraction (EBSD) & X‐ray diffraction (XRD), Euler angles are still generally used to import and export data. However, because of the lack of standard definitions for the unit cell reference settings and specimen axes, several transformation descriptions
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