A Simplified Model for the Secular Dynamics of a Parametrically-Excited Magnetic Micro-Particle

Magnetic micro-particles find numerous applications as the end-effectors in micro-manipulation technologies. A recent micro-manipulation technology proposed the use of micro-ring actuators and parametric excitation to trap magnetic particles in three-dimensions (3-D). Here, a simplified linear time-invariant system model is proposed to describe the secular dynamics of such particles. First, the exact dynamic equations are obtained for the case of a particle oriented upwards and the procedure to obtain their approximate solution is described. The obtained approximate response is employed to subsequently propose a simple linear time-invariant system model for the secular dynamics of the particle. Next, the same approach is extended for the case of a magnetic particle with arbitrary orientation. In both cases the results of the simplified model are compared with numerical solutions of the exact system equations. The two are found to match with an accuracy of over 99.6%.