Saddle in linear curl forces, cofactor systems and holomorphic structure

We show the connection between the theory of Hamiltonian curl forces introduced by Berry and Shukla and the cofactor systems introduced by the Linköping school. The linear curl forces studied by Berry and Shukla are the dynamics related to saddle potentials. We also discuss the rotating saddle potential and its connection to the Bateman-like Lagrangian for a pair of damped and anti-damped oscillators. Here the pair of frictional terms can be mapped to the Coriolis-like force caused by the rotation of the potential as shown by Kirillov and Levi. We study the geometrical structure of the linear curl force. A hidden holomorphic structure is uncovered in this paper.