EU Regiona School - Hesch Seminar
Dr. Hesch - Introduction to Rigid Body Dynamics
University of Siegen
The analytical treatise of rigid bodies has been subject to research for centuries. During the past decades various approaches starting form generalized coordinates, quaternions and nowadays a natural coordinate description has been developed, suitable for the numerical treatise on modern computer architecture. The present talks deals with a uniform approach for the spatial discretization of struc- tural elements. In particular, it is shown that a uniform set of differential-algebraic equations (DAEs) with constant mass matrix governs the motion of rigid bodies and semi-discrete formulations of structural components resulting from a finite element dis- cretization in space.
The simple structure of the DAEs makes possible the design of structure-preserving time integrators. Both energy-momentum schemes popular in nonlinear structural dynamics as well as symplectic-momentum variational integrators can be applied in a straight forward manner .