Citation

Xin G. Am. J. Traffic Transp. Eng. 2023; 8(4): 99-104.

Copyright

(Copyright © 2023, Science Publishing Group)

DOI

10.11648/j.ajtte.20230804.13

PMID

unavailable

Abstract

The kinematics equations of longitude and latitude have singularities in polar of the earth. To solve the problem, a solution called the quaternion form of longitude, latitude and heading kinematics equations was created and introduced in the paper. The key point of the solution is to define an instantaneous great circle for a moving particle. To a moving particle, it is impossible to define three definite Euler angles, thus the definite quaternion to it does not exist. But to the instantaneous great circle, three definite Euler angles can be defined. Meanwhile, the instantaneous great circle is rotating by driving of the moving particle, thus quaternion can be used to model the instantaneous great circle. The model is the kinematics equations of longitude, latitude and heading in quaternion form. This form of equations can be used all over of the earth. It works well on the polar of the earth automatically. Verifying by mathematics simulation has been designed and practiced. The simulation includes some flights around the earth with flying by the polar and turning in polar region. The results of simulation suggest that the flight plan can be executed precisely by the algorithm. The solution can be applied in fields of flight simulation and inertial navigation.

Language: en