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International Journal of Aerospace Engineering
Volume 2015, Article ID 904913, 11 pages
Research Article

Cone Algorithm of Spinning Vehicles under Dynamic Coning Environment

1School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
2Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, Beijing 100081, China
3Beijing Key Laboratory of High Dynamic Navigation Technology, Beijing Information Science & Technology University, Beijing 100101, China

Received 20 August 2015; Revised 30 October 2015; Accepted 10 November 2015

Academic Editor: Hikmat Asadov

Copyright © 2015 Shuang-biao Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Due to the fact that attitude error of vehicles has an intense trend of divergence when vehicles undergo worsening coning environment, in this paper, the model of dynamic coning environment is derived firstly. Then, through investigation of the effect on Euler attitude algorithm for the equivalency of traditional attitude algorithm, it is found that attitude error is actually the roll angle error including drifting error and oscillating error, which is induced directly by dynamic coning environment and further affects the pitch angle and yaw angle through transferring. Based on definition of the cone frame and cone attitude, a cone algorithm is proposed by rotation relationship to calculate cone attitude, and the relationship between cone attitude and Euler attitude of spinning vehicle is established. Through numerical simulations with different conditions of dynamic coning environment, it is shown that the induced error of Euler attitude fluctuates by the variation of precession and nutation, especially by that of nutation, and the oscillating frequency of roll angle error is twice that of pitch angle error and yaw angle error. In addition, the rotation angle is more competent to describe the spinning process of vehicles under coning environment than Euler angle gamma, and the real pitch angle and yaw angle are calculated finally.