Parameterizing the eye movement dynamics on LIST and SO(3): How to move the singularities away

Using a suitable parametrization, the dynamics of eye rotation can be written as an Euler Lagrange equation on LIST or SO(3) depending on whether eye is assumed to satisfy the Listing's constraint or not. The equations typically have singularities and we show in this paper that by choosing alternate forms of the state variables, the singularities can be moved, for example from the frontal gaze to the backward gaze direction in the case of LIST. Similar constructions are also possible on SO(3).