  A parameterization is described for quantifying translational motion of a
point in three-dimensional Euclidean space. The parameterization is similar to
well-known parameterizations such as spherical coordinates in that both
position and velocity are decoupled into magnitude and orientation components.
Unlike these standard parameterizations, where principal rotation sequences are
employed, the method presented in this research employs Euler parameters. By
using Euler parameters instead of Euler angles, singularities and trigonometric
functions are removed from the equations of motion. The parameterization is
demonstrated on two examples, where it is found that the new parameterization
offers both mathematical and computational advantages over other commonly used
parameterizations.
