Quaternions and Vector Mapping in Three-Dimensional Space

Gui San Li

doi:10.4028/www.scientific.net/AMM.235.101

Paper Titles

Judgement Research on the Dump Truck Frame Intensity-Mass Relationship Based on Fuzzy Theory
p.79

α Extension of the Cubic Ball Curve
p.85

Numerical Simulation and Experimental Verification of a Vertical Jet in Swirling Cross-Flow
p.90

Research on Welding Repair for Tee Joint Crack of Final Superheater Header of 300MW Station Boiler
p.96

Quaternions and Vector Mapping in Three-Dimensional Space
p.101

The Optimal Regulations of the Interconnection-Degrees of Large Scale Systems under Instable Case
p.107

A Threat Sorting Approach Based on the Fuzzy Beliefs
p.111

Asymptotic Properties of Neutral Stochastic Functional Differential Equations with Infinite Delay
p.119

3D Virtual Simulation of Beam Pumping Unit Motion Based on Inverse Kinematic
p.124

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 235Quaternions and Vector Mapping in...

Quaternions and Vector Mapping in Three-Dimensional Space

Abstract:

On the basis of analyzing the relations between vector operation and properties of multiplication operation of quaternions, the geometric representation and mapping of quaternions and vectors defined in three-dimensional space are established. The mathmatic operation of space vector, in addition to any space unit vector, rotating around three coordinate axises is carried based on the utilization of quaternions.The main purpose of this paper is to solve the issues of mathmatic tools introduced in spatial mechanism analysises and integrations by making use of quatnions.

You might also be interested in these eBooks

Advances in Computing, Control and Industrial Engineering

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volume 235)

Pages:

101-106

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.235.101

Citation:

Cite this paper

Online since:

November 2012

Authors:

Gui San Li

Keywords:

Mapping, Mathmatic Tools, Quatnions, Spatial Mechanism, Vector

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] Xiangke Wang , Dapeng Han, Changbin Yu, Zhiqiang Zheng: The geometric structure of unit dual quaternion with application in kinematic control, J. Math. Anal. Appl. 389 (2012) 1352–1364.

DOI: 10.1016/j.jmaa.2012.01.016

Google Scholar

[2] E. Zupan, M. Saje, D. Zupan: The quaternion-based three-dimensional beam theory, Comput. Methods Appl. Mech. Engrg. 198 (2009) 3944–3956.

DOI: 10.1016/j.cma.2009.09.002

Google Scholar

[3] Timothy Barfoot _, JamesR. Forbes, PaulT. Furgale: Pose estimation using linearized rotations and quaternion algebra, Acta Astronautica 68 (2011) 101–112.

DOI: 10.1016/j.actaastro.2010.06.049

Google Scholar

[4] Mengke Chen, Guisan Li: Motion Analysis to RSSR by Expanding Vector Property Plural. Coal Mine Machinery, 2007. 5.

Google Scholar

[5] LiZhong: Story of the Plural, Science Press, Beijing 2011, 6.

Google Scholar