Abstract
Abstract
A new presentation of global inertia tensors is given in the form of a 4 × 4 matrix, putting together all the inertia characteristics of a generalized body. It leads to a very condensed form of the inertia coefficients (coefficients of the kinetic energy matrix and Christoffel's symbols), which are present in the equations of motion. This theory offers a systematic method for obtaining the dynamic model of multibody systems (rigid bodies), in which only matrix products appear, generated by the use of homogeneous coordinates. Furthermore, the mathematical developments are made in the framework of general complex joints, allowing a one degree-offreedom relative motion, and treat the case of pseudo-parameters, which have non-holonomic properties. As examples, the main results of the derivative-free computations of the dynamic model are given for a free solid and a simplified model of a car.
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