This paper is concerned with the integration of the differential equations for the Euler parameters, for the purpose of describing the orientation of a rigid body. This can be done using standard methods, but in some cases, such as in the presence of impulsive forces, the angular velocities are not continuous and methods based on high order continuity are not appropriate. In this paper, the use of the closed-form solution for piecewise constant angular velocity as the basis for a computational algorithm is studied. It is seen that if this solution is implemented in a leapfrog manner a method with second-order accuracy is obtained in the smooth case, while this method also makes sense in the discontinuous case.
A Note on the Computation of the Euler Parameters
Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript Received by the Dynamics Systems and Control Division July 10, 2000. Associate Editor: Y. Hurmuzlu.
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Johansson , L. (July 10, 2000). "A Note on the Computation of the Euler Parameters ." ASME. J. Dyn. Sys., Meas., Control. December 2001; 123(4): 719–722. https://doi.org/10.1115/1.1408943
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