The dynamical study of the current and sudden motions of the rigid body and multibody systems (MBS), as example the mechanical robot structure, and in accordance with differential principles typical to analytical dynamics of systems, is based, among others, on the advanced notions, such as momentum and angular momentum, kinetic energy, acceleration energies of different orders and their absolute time derivatives of higher order. Advanced notions are developed in the direct connection with the generalized variables, also named independent parameters corresponding to holonomic mechanical systems. But, the expressions of definition of the advanced notions contain on the one hand kinematical parameters and their differential transformations, corresponding to absolute motions, on the other hand the mass properties. By means of the especially researches of the author, in this paper will be presented reformulations and formulations concerning the classical notions and theorems from dynamics. In the following the study will be extended on the energies of higher order. So, the expressions of definition in explicit form will be presented for the acceleration energy of first, second and third order. They are corresponding to the current and sudden motions of rigid body and multi body systems. These formulations will also contain the absolute time derivatives of higher order of the advanced notions, according to differential equations of higher order, typically to analytical dynamics of systems.

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