Teodor Alfson: On Eye Movement in Hamiltonian Formalism

Abstract: Listing's law governs many of the movements of the human eye. In this paper we study the eye under a symmetric rigid body model, and explore the implications of Listing's law. We look at different representations of the group of rotations in three dimensional space, as well as provide a background of rotational mechanics. Optimal control theory is introduced and used to find geodesics of the unit sphere in four dimensional space, and for the motions of the eye satisfying Listing's constraint.