B Karasozen, P, Rentrop, Y. Wagner

The planar inverted $n$-bar model and its multibody formulation are presented. The descriptor formulation, which is based on a set of redundant coordinates, results in a differential-algebraic (DAE) system of index $3$. A minimum set of coordinates characterizes the state space formulation, which corresponds to an ordinary differential equation (ODE) system. The regular structure of the descriptor form allows a complete formulation of the equations of motion. On this base, by induction arguments the state space form can be derived analytically. We present these equations, since the inverted $n$-bar model serves as an instructive example for the drift phenomena in numerical simulation, for the design of a controller and for the balancing problem in the context of neural networks.

Keywords: descriptor form, multibody systems, state space form