Matrix Formulation of Rigid Body Dynamics
Résumé
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 $4\times 4$ positive definite symmetric matrix. The translation vector and the rotation matrix of the rigid body are also gathered in a $4\times 4$ matrix. Therefore the motion equations are formulated as an equality between 4x4 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 4x4 symmetric matrices.