Towards a compact and computer-adapted formulation of the dynamics and stability of multi rigid body systems

Abstract

The dynamics of rigid bodies coupled by homonymic and non-homonymic constraints are formulated by the Newton - Euler method - employing a compact notation. The compact notation involves the use of two three by three matrices A and ? and the totality of constraint vector C. The Lagrangian and Newton - Euler methods are related for a one - link rigid body in order to introduce the methodology of the paper in full detail. Stability and control of the resulting nonlinear systems are investigated by the use of Lyapunov methods. Digital computer simulations of typical movements are carried out in order to demonstrate feasibility of the formulation and the approach.