On the Transitivity Equations of Rigid-Body Dynamics

This paper presents direct derivations of the various forms of the famous transitivity equations of rigid-body kinematics from a simple and unified viewpoint. These forms are indispensable in the derivation of the Eulerian (gyro) equations of motion via the Lagrangean (analytical mechanics) method. Both true (holonomic) and quasi (nonholonomic) coordinate forms are presented. A vectorial derivation of the Eulerian equations from the Central Equation and from Hamilton’s Principle is also included in the Appendix.