A short document discusses the general problem of mathematical modeling of the three-dimensional rotational dynamics of rigid bodies and of the use of Euler parameters to eliminate the singularities occasioned by the use of Euler angles in such modeling. The document goes on to characterize a Hamiltonian model, developed by the authors, that utilizes the Euler parameters and, hence, is suitable for use in computational simulations that involve arbitrary rotational motion. In this formulation unlike in prior Eulerparameter- based formulations, there are no algebraic constraints. This formulation includes a general potential-energy function, incorporates a minimum set of momentum variables, and takes an explicit state-space form convenient for numerical implementation.

Practical application of this formulation has been demonstrated by the development of a new and simplified model of the rotational motion of a rigid rotor to which is attached a partially filled mercury ring damper. Models like this one are used in guidance and control of spin-stabilized spacecraft and gyroscope-stabilized seekers in guided missiles.

This work was done by Eric P. Fahrenthold and Ravishankar Shivarma of the University of Texas for Johnson Space Center. For more information, download the Technical Support Package (free white paper) at www.techbriefs.com/tsp under the Infor - mation Sciences category. MSC-23830-1


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This article first appeared in the November, 2009 issue of NASA Tech Briefs Magazine.

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