Abstract Louis Poinsot’s result, that any relative rotational motion between two frames can be realized as the motion of a moving cone rolling without slipping on a stationary cone, is stated and proved using matrix-vector algebra. Poinsot’s result is used to obtain a characterization of all attitude trajectories that are closed in the sense that the trajectory terminates at the same point that it starts from. The characterization is an extension to the continuous case of results on discrete closed sequences of rotations, and yields examples of closed attitude (orientation and angular velocity vector) trajectories that may be seen as extensions to the continuous-time case of classical theorems on discrete rotation sequences by Rodrigues, Hamilton and Donkin. One of the examples of closed attitude trajectories is used to obtain an extension of the Goodman–Robinson theorem, which reconstructs the instantaneous orientation of a rotating frame from the components of a fixed vector taken along this frame. This extension yields an explicit expression for the rotation matrix representing the instantaneous orientation of a torque-free rigid body in terms of the body components of its angular velocity.
Rolling Cones, Closed Attitude Trajectories, and Attitude Reconstruction
The Journal of the Astronautical Sciences ; 65 , 3 ; 261-290
2018-09-15
30 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Poinsot’s construction , Rolling cones , Rodrigues–Hamilton theorem , Donkin’s theorem , Goodman–Robinson theorem , Rigid-body phase , Attitude reconstruction Engineering , Aerospace Technology and Astronautics , Mathematical Applications in the Physical Sciences , Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics)
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