نتایج جستجو برای: quaternions

تعداد نتایج: 1307  

2007
Basile Graf

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...

2009
J P Singh

Using quaternions, we study the geometry of the single and two qubit states of quantum entanglement. Through the Hopf fibrations, we identify geometric manifestations of the separability and entanglement of two qubit quantum systems.

1995
Stefano De Leo

We reformulate Special Relativity by a quaternionic algebra on reals. Using real linear quaternions, we show that previous difficulties, concerning the appropriate transformations on the 3 + 1 space-time, may be overcome. This implies that a complexified quaternionic version of Special Relativity is a choice and not a necessity. a) e-mail: [email protected]

2008
J. P. Singh S. Prabakaran

Using quaternions, we study the geometry of the single and two qubit states of quantum computing. Through the Hopf fibrations, we identify geometric manifestations of the separability and entanglement of two qubit quantum systems. c © Electronic Journal of Theoretical Physics. All rights reserved.

2017
Morten Engell-Nørreg̊ard Kenny Erleben

In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection. The three methods are described in some detail. An analysis is performed where the three methods ar...

2015
Yan-Bin Jia

Up until now we have learned that a rotation in R3 about an axis through the origin can be represented by a 3×3 orthogonal matrix with determinant 1. However, the matrix representation seems redundant because only four of its nine elements are independent. Also the geometric interpretation of such a matrix is not clear until we carry out several steps of calculation to extract the rotation axis...

1995
STEFANO DE LEO

We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyse possible quaternionic groups for GUTs.

2013
Josué C. dos Santos Maria Cećılia Zanardi Nicholas Matos

This study at aims performing the stability analysis of the rotational motion to artificial satellites using quaternions to describe the satellite attitude (orientation on the space). In the system of rotational motion equations, which is composed by four kinematic equations of the quaternions and by the three Euler equations in terms of the rotational spin components. The influence of the grav...

2004
Tony Barrera Anders Hast Ewert Bengtsson

Animation is often done by setting up a sequence of key orientations, represented by quaternions. The in between orientations are obtained by spherical linear interpolation (SLERP) of the quaternions, which then can be used to rotate the objects. However, SLERP involves the computation of trigonometric functions, which are computationally expensive. Since it is often required that the angle bet...

2010
N. C POWERS

The main result is that any continuous real-linear operator A on a quaternionic Hubert space has a unique decomposition A=A0+iiAl + izAi+iiA3, where the A„ are continuous linear operators and (fi,f2,'3) is any right-handed orthonormal triad of vector quaternions. Other results concern the place of the colinear and complex-linear operators in this characterisation and the effect on the Av of a r...

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