The Inverted N-Bar Model in Descriptor and State Space Form

B. Karasozen, P. Rentrop, Y. Wagner

• cited by B. Simeon, MBSPACK-numerical integration software for constrained mechanical motion, "Surveys on Mathematics for Industry", 5, pp. 169-202 , 1995
• cited by B. Simeon, Modelling a Flexible Slider Crank Mechanism by a Mixed System of DAEs and PDEs, "Mechanical Modelling of Systems", 2, pp. 1-18, 1996

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.

1991 Mathematics Subject Classification Primary 65L05, 65L99, 70B10

KEYWORDS: descriptor form, multibody systems, state space form