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.