Use of cholesky coordinates and the absolute nodal coordinate formulation in the computer simulation of flexible multibody systems

In a previous publication, procedures that can be used with the absolute nodal coordinate formulation to solve the dynamic problems of flexible multibody systems were proposed. One of these procedures is based on the Cholesky decomposition. By utilizing the fact that the absolute nodal coordinate formulation leads to a constant mass matrix, a Cholesky decomposition is used to obtain a constant velocity transformation matrix. This velocity transformation is used to express the absolute nodal coordinates in terms of the generalized Cholesky coordinates. The inertia matrix associated with the Cholesky coordinates is the identity matrix, and therefore, an optimum sparse matrix structure can be obtained for the augmented multibody equations of motion. The implementation of a computer procedure based on the absolute nodal coordinate formulation and Cholesky coordinates is discussed in this paper. Numerical examples are presented in order to demonstrate the use of Cholesky coordinates in the simulation of the large deformations in flexible multibody applications.