Three-dimensional MEMS simulation using Euler parameters

Lumped-constant simulation of microelectromechanical systems (MEMS) is performed by solving numerically systems of coupled ordinary differential equations expressing Kirchhoff´s laws and those of classical mechanics. One of the challenges is to describe mathematically the dynamics of these systems in a form that is both numerically stable and computationally efficient. The goal of this paper is to show that the representation of rigid-body dynamics based on the Euler parameters satisfies these requirements: it can describe arbitrary three-dimensional motion, its numerical stability properties are superior to those of other more frequently used parametrizations, and it can be implemented in a simulator in an efficient manner using so-called element stamps.