FORMULATIONS ON INPUT PARAMETERS IN ADVANCED DYNAMICS

The dynamical study of the rigid body and multibody systems, in accordance with fundamental theorems and differential principles typical to analytical dynamics, is based on advanced notions, such as: momentum, angular momentum, kinetic energy, acceleration energies of different orders and their absolute time derivatives of higher order. Advanced notions and theorems are developed in connection with the generalized variables, also named independent parameters of position and orientation (d.o.f.), corresponding to holonomic rigid body and systems. But, mechanically, the expressions of definition of the advanced notions are based on fundamental input parameters. These are referring on the one hand to kinematical parameters and their differential transformations, corresponding to absolute motions, on the other hand to mass properties highlighted by mass and inertial tensor, as well their generalized variation laws. By means of the researches of the author, based on classical transformations and matrix exponentials, in this paper a few essential formulations concerning input expressions and parameters from advanced kinematics and dynamics will be presented. They become input expressions compulsory included in fundamental notions and theorems, in the differential principles typical to analytical mechanics, as well as in the dynamics equations of higher order, corresponding to the current and sudden motions in the case of the rigid body and multibody systems, as example robot structures.