NEW APPROACHES ON NOTIONS FROM ADVANCED MECHANICS

The dynamical study of the current and sudden motions of the rigid body, and in accordance with differential principles typical to analytical dynamics of systems, is based, between others, on advanced notions, such as: angular momentum, kinetic energy, acceleration energies of different orders and their absolute time derivatives of higher order. Advanced notions are developed in connection with the generalized variables, also named independent parameters of position and orientation corresponding to holonomic rigid body. But, mechanically, 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, highlighted by mass and inertial tensors and their generalized laws. By means of the researches of the author, in this paper a few essential reformulations and new formulations concerning input expressions and parameters from advanced kinematics and dynamics will be presented.  They become input expressions compulsory included in dynamics equations of higher order, corresponding to the current and sudden motions in the case of the rigid body. These are extended on the multibody systems. Within of the paper a few reformulations on the fundamental theorems from dynamics, differential generalized principle in analytical dynamics, as well as generalization of Gibbs – Appell’s equations will be also defined.