Frequency Domain Characteristics in Nonlinear Trimmer Dynamics

We analyse a dynamical system describing the movement of the blade of a hair trimmer. Using nondimensionalisation and perturbation methods, we systematically analyse this model, with the goal of explaining a dip in the current amplitude observed in numerical simulations. We find that the motion of the blade is controlled by seven dimensionless parameters, and the dip in amplitude of the current corresponds to one of the dimensionless parameter groups taking the value of one. There is excellent agreement between our asymptotic solutions and long-time behaviour of the model revealed by numerical simulation.