ADVANCED EQUATIONS 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 on the advanced notions, such as: generalized forces, 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 advanced equations of dynamics contain on the one hand advanced notions from kinematics and their differential transformations, typically to absolute motions, and on the other hand mass properties and generalized forces.
By means of the especially researches of the author, within of this paper will be presented reformulations and new formulations concerning the advanced kinematics parameters, as well as polynomial interpolating functions of higher order. In the following of the paper a few reformulations on fundamental theorems of dynamics and differential generalized principle of analytical dynamics will be presented. But, the fundamental aspect of this paper will consist in the fact that the author of the paper will propose generalized differential equations of higher order for any sudden and transitory motion. These equations contain acceleration energies of higher orders in generalized mathematical form.
Key words: analytical dynamics, mechanics, advanced notions, advanced dynamics equations, robotics.
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