  Three parameterizations are developed for modeling translational motion of a
point mass in atmosphere flight over a central rotating body. Unlike well-known
parameterizations such as spherical coordinate parameterizations, where
position and velocity are parameterized using a magnitude an an Euler angle
rotation sequence, the method presented in this research employs Euler
parameters. Consequently, singularities and trigonometric functions are
eliminated from the differential equations of motion. As a result, the new
parameterizations presented in this paper offer computational advantages over
standard parameterizations that employ Euler angle sequences. Finally, an
example is studied where an atmospheric vehicle moves while in vertical flight,
demonstrating the nonsingular nature of the formulations developed in this
paper.
