منابع مشابه
Pexiderized functional equations for vector products and quaternions
The purpose of the present paper is to solve the pexiderized versions of functional equations investigated by B. Nyul and G. Nyul [2], raised by the connection between products of quaternions and products of three-dimensional vectors. 1 Quaternionic products and vector products Let H = {r+ x1i+ x2j + x3k | r, x1, x2, x3 ∈ R} be the skew field of quaternions with the basic relations i2 = j2 = k2...
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Mathematics requires three markers to define a local coordinate system to calculate rotations in three dimensions (3D), as three coordinates are necessary to specify the orientation of a rigid body with respect to a fixed set of space axes. However, it is not uncommon in wheelchair literature to find papers (Veeger, et al., 1991) that used only two markers to define segment rotation in three di...
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This paper describes new issues of the Mathematica standard package Quaternions for implementing Hamilton’s Quaternion Algebra. This work attempts to endow the original package with the ability to perform operations on symbolic expressions involving quaternion-valued functions. A collection of new functions is introduced in order to provide basic mathematical tools necessary for dealing with re...
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Vertices of the 4-dimensional semi-regular polytope, the grand antiprism and its symmetry group of order 400 are represented in terms of quaternions with unit norm. It follows from the icosian representation of the E8 root system which decomposes into two copies of the root system of H4. The symmetry of the grand antiprism is a maximal subgroup of the Coxeter groupW (H4). It is the groupAut(H2⊕...
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We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more complex models, for instance, the one of a satellite with inertial wheels and expressed in a non-inertial reference frame. As it is well known, one nice advanta...
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ژورنال
عنوان ژورنال: Nature
سال: 1893
ISSN: 0028-0836,1476-4687
DOI: 10.1038/048364b0