ADVANCED NOTIONS IN ANALYTICAL DYNAMICS OF SYSTEMS
The dynamical study of the current and sudden motions of the 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: 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, 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 mass center, inertial tensors and their generalized laws, as well as pseudoinertial tensors.
By means of the especially researches of the author, in this paper will be presented reformulations and new formulations concerning the advanced kinematics parameters, as well as advanced notions such as: kinetic energy and acceleration energies of different orders in explicit and matrix form. They are corresponding to the current and sudden motions of MBS. 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.
Key words: analytical dynamics, mechanics, advanced notions, dynamics equations, robotics.
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