Closed form solution for p-curves in SO(4)

This paper describes the solution for p-curves in SO(4) and gives its closed form. The rotational symmetry was exploited in order to simplify the algebra. The relationship between the Casimir invariant functions and Lax operator is provided, along with its use as part of a Lax pair. The double cover by SU(2) × SU(2) enables two simpler problems to be found and integrated using Philip Hall coordinates and the solutions are then projected onto SO(4). The methodology is generic and can be applied to other problems.