Quaternion and Its Application in Rotation Using Sets of Regions


  • Logah Perumal


This paper is written to aid the readers to understand application of Euler angles and quaternion in representing rotation of a body in 3-dimensional Euclidean space,3ℜ. Application of quaternion would later require conversion of the quaternion to Euler angles. This is to enable quaternion to be compatible with other applications which use Euler rotation sequence to represent rotation. Thus, a framework to convert a quaternion, which is produced from a random rotation sequence to Euler angles with any specified rotation sequence is proposed and demonstrated here, to aid practitioners to use quaternion in their applications. This will also enable quaternion to be applied in arbitrary sequence onto applications developed using certain rotation sequence of Euler angles. Finally, a program is developed using Matlab-simulink software to demonstrate application of quaternion in maneuvering orientation of a missile flying in 3D space. Six degree of freedom (6DoF) block, which employs Euler rotation sequence of XYZ, is used to aid users to graphically see the maneuvering of the missile’s orientation as it flies in 3-dimensional Euclidean space. Quaternion, which is produced from random rotation sequence keyed in by the user, is converted to Euler angles with rotation sequence XYZ by using the proposed method.


Eric M. Jones and Paul Fjeld, “Gimbal angles, gimbal lock, and a forth gimbal for christmas,” http://www.hq.nasa.gov/alsj/gimbals.html, April 29, 2011.

W.R. Hamilton, “On a new species of imaginary quantities connected with a theory of quaternions,” Proc. of the Royal Irish Academy, vol. 2, 1844, pp. 424-434.

David H. Eberly, and Ken Shoemake, Game physics morgan kaufmann, pp. 507-544, 2004.

James Jennings, “Towards an intuitive understanding of quaternion rotations,” Quantum, 2008.

Andrew J. Hanson, Visualizing quaternions, Morgan Kaufmann Series, Canada, 2006.

“Euler angles,”http://goo.gl/Uo0Nm.

“Inertial navigation system,” http://goo.gl/u3JHI.

James Diebel, “Representing attitude: Euler angles, Unit Quaternions, and Rotation Vectors,” Matrix, Citeseer, 2006.

Sung-Sik Shin, Jung-Hoon Lee and Sug-Joon Yoon, “A comparison study of real-time solution to all attitude angles of an aircraft,” Journal of Mechanical Science and Technology, vol. 20, no. 3, pp.376-381, 2006.

B. Alpern, L. Carter, M. Grayson, and C. Pelkie, “Orientation maps: techniques for visualizing rotations (a consumer’s guide),” IEEE Conference on Visualization, 1993, pp. 183-188.

Andy “Maths - Euler angles,” http://goo.gl/D9Agt.




How to Cite

L. Perumal, “Quaternion and Its Application in Rotation Using Sets of Regions”, Int. j. eng. technol. innov., vol. 1, no. 1, pp. 35–52, Oct. 2011.