Quaternions and the rotation of a rigid body

Details Quaternions and the rotation of a rigid body Quaternions and the rotation of a rigid body

Nov 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cemda..96..239a&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 96, Issue 3-4, pp. 239-251

Astronomy and Astrophysics

Astronomy

4

Attitude Dynamics, Rigid Body Motion, Rotations, Quaternions

Scientific paper

The orientation of an arbitrary rigid body is specified in terms of a quaternion based upon a set of four Euler parameters. A corresponding set of four generalized angular momentum variables is derived (another quaternion) and then used to replace the usual three-component angular velocity vector to specify the rate by which the orientation of the body with respect to an inertial frame changes. The use of these two quaternions, coordinates and conjugate moments, naturally leads to a formulation of rigid-body rotational dynamics in terms of a system of eight coupled first-order differential equations involving the four Euler parameters and the four conjugate momenta. The equations are formally simple, easy to handle and free of singularities. Furthermore, integration is fast, since only arithmetic operations are involved.

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