Matrix formulation of the motion equations of a rigid body and identification of the ten inertia characteristics

Abstract

The motion equations of a rigid body involve ten inertial characteristics: the mass, the mass center position and the inertia matrix. In order to identify these ten inertia characteristics, we propose an approach unifying them in a 4 × 4 positive definite symmetric matrix. The translation vector and the rotation matrix of the rigid body are also gathered in a 4 × 4 matrix. Therefore the motion equations are formulated as an equality between 4 × 4 skew–symmetric matrices: one representing the sum of external forces and torques, the second representing the dynamic force and torque. The identification is performed by a projected conjugate gradient algorithm developped in the 10–dimensional linear space of 4 × 4 symmetric matrices. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)