Calculation of the principal moment of inertia and Euler angles of the centre inertia principal axis system: design and implementation of the algorithm

Abstract

To overcome the lack of algorithms and programs in the literature about the principal moment of inertia and Euler angles of the centre inertia principal axis system for the closest to the original coordinates, the theories and methods of linear algebra are applied to transform of the inertia matrix between coordinate systems. The algorithms are designed to solve Euler angles on the centre inertia principal axis of the closest to the original coordinate system according to the definition of direction cosine matrix. Lastly, calculation program is developed using the algorithms based on MATLAB. Compared with ADAMS, the program by using the algorithms gets the same results with ADAMS, which verified the correctness and effectiveness of the algorithms. It is the important requisites in the torque roll axis decoupling to obtain an accurate main moment of inertia and the centre inertia principal axis.