Note on Ruijsenaars–Schneider Model

We propose a simple formulation of the Ruijsenaars–Schneider (RS) model based on the twisted Poisson brackets that are usually used to describe particles moving in an external magnetic field. Then, starting from this formulation, we propose the system with dynamical \(2d\) Poincaré symmetry, which is described by the same Hamiltonian and the twisted Poisson brackets corresponding to the motion in an almost generic magnetic field.