By Adam Morawiec
ISBN-10: 3642073867
ISBN-13: 9783642073861
ISBN-10: 3662091569
ISBN-13: 9783662091562
The e-book is ready mathematical and computational foundations of texture research. Numerical ideas are critical in texture research, so the ebook is basically addressed to researchers and scholars utilizing those strategies in practice.
Orientations and Rotations is particularly various from different books on textures in its content material and point of interest. significant a part of the ebook is dedicated to orientations and rotations in most cases. commencing chapters comprise an in depth and thorough advent to rotations in 3 dimensions (including parameterizations and geometry of the rotation space). extra chapters also are normal yet they are going to be of curiosity for readers facing orientations of symmetric items. This topic is vital for crystallographic textures considering that so much crystal constructions are symmetric. the ultimate chapters situation more effective elements of textures (such because the selection of orientations from diffraction styles and the calculation of powerful elastic houses of polycrystals).
The e-book may be of curiosity for scientists engaged on plasticity, grain obstacles, recrystallisation, grain development, and diverse different concerns during which textures has to be taken under consideration. end result of the broad elements on rotations normally, the e-book may be beneficial for everybody facing rotations
Read Online or Download Orientations and Rotations: Computations in Crystallographic Textures PDF
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Extra info for Orientations and Rotations: Computations in Crystallographic Textures
Sample text
It is trivial to check that (hkl)· [uvw] = (h k - (h + k) l). [2uv 2v - u - (u + v) 3w]/3, where the . operation is defined as the sum of products of corresponding array elements. 98) or Frank, 1965. 10 Computational Properties of Parameterizations Analysis of textures often requires large scale computations. The question arises about most advantageous choice of parameters. Besides the conceptual suitability to a considered problem, one would like the parameters to guarantee robust, accurate and effective (in terms of the execution time) computations.
This time the answer is positive. , with coefficients satisfying d = a, c = -b and aa + bb = 1. 31), we get x' = Ox, where ~(a2+a2_b2_b2)~(a2_a2+b2_b2) (ab+ab)] 0= [ ~(-a2+a2+b~-b2)~(a2+a2+b~+b2)_i(ab_a~) . 34) Direct calculation confirms that the matrix 0 is special orthogonal and thus, the transformation is a proper rotation. The interrelated complex numbers a, b, c and d are referred to as Cayley-Klein parameters of a rotation. Since a and b satisfy the condition aa + bb = 1, only three independent real numbers are involved.
The direction of the rotation axis is expressed via quaternion components by The inverse formulas are also simple. 18) between the trace of the rotation matrix and the rotation angle w gives qO = ± Icos(w/2)1. 45) leads to the relation qi = ±J3 - O jk Okj/(2(Oll + 1)1/2)ni' which can be transformed to qi = ± Isin(w/2)1 ni' With w in the range [0,7f], the values ofsin(w/2) and cos(w /2) are non-negative and the quaternion components can be expressed as qO = ± cos(w /2) and qi = ± sin(w /2)ni . 47) 38 2 Parameterizations Fig.
Orientations and Rotations: Computations in Crystallographic Textures by Adam Morawiec
by Charles
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