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Attitude Kinematics Using Slewing Transformation of a Single Axis
Advances in Space Research ( IF 1.746 ) Pub Date : 2020-05-21 , DOI: 10.1016/j.asr.2020.05.017
Russell P. Patera

Attitude kinematics using a single axis was developed to establish the relationships among the axis trajectory, enclosed solid angle and the associated attitude transformation. An arbitrary transformation due to a sequence of finite rotations or due to propagation consisting of an infinite number of infinitesimal rotations is equivalent to the product of a slewing transformation along a great circle arc linking the initial and final orientations of the axis followed by a rotational transformation about the axis. A key finding of this work is that the slewing transformation commutes with the rotational transformation, if the trajectory of the slewing transformation is fixed in space and the axis orientation is accounted for in the rotational transformation. The results were used to establish two new kinematic theorems. The new theorems provided simple derivations of Ishlinskii’s theorem, the Goodman-Roberson theorem and a result found by Montgomery. The findings in this work were applied to attitude propagation by separating attitude rotational increments that are normal to the axis with those that are parallel to the axis. The normal and parallel angular increments were integrated separately to form the slewing transformation and rotational transformation, respectively. The product of the two commuting transformations formed the total propagation transformation. The findings were validated by using them to create and implement a propagation algorithm. Numerical testing showed that the new algorithm has accuracy comparable to traditional attitude propagation algorithms when stress tested with pure coning motion.
更新日期:2020-05-21

 

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