On the Stability of Symmetric Periodic Orbits of a Comb-Drive Finger Actuator Model

Abstract: In this paper, we study the stability of symmetric periodic solutions of the comb-drive finger actuator model. First, on the basis of the relationship between the potential and the period as a function of the energy, we derive the properties of the period of the solution of the corresponding autonomous system (the parameter $\delta$ of input voltage $V_\delta(t)$ is equal to zero) in the prescribed energy range. Then, using these properties and the stability criteria of symmetric periodic solutions of the time-periodic Newtonian equation, we analytically prove the linear stability/instability of the symmetric $(m,p)$-periodic solutions which emanated from nonconstant periodic solutions of the corresponding autonomous system when the parameter $\delta$ is small.