MASS DISTRIBUTION IN ANALYTICAL DYNAMICS OF SYSTEMS

Abstract: In the case of the multibody systems (MBS), as example the mechanical robot structure, a few simplifying hypotheses, referring to mass properties, are implemented. According to these, the mass properties are continuously distributed between the fixed basis and the last kinetic ensemble from mechanical structure. As a result, in the dynamical study of MBS, the author of the paper has introduced the phrase “mass distribution” instead of mass geometry, typically too rigid solid. Mass distribution is based on the mass as fundamental notions in analytical dynamics of systems. At its turn, mass together with energy highlight the matter notion. But, mass is also highlighted by means of the two properties: gravitation and inertia. According to fundamental theorems from Newtonian dynamics, in the case of the translation motion the inertia property is highlighted by mass and position of the mass center. In the case of the resultant rotation motion the inertia property is characterized by mechanical moments of inertia and extension of these properties, known as inertial tensors and pseudoinertial tensors. Their matrix expressions are compulsory included in the dynamical notions like: kinetic energy, acceleration energy, angular momentum and their time derivatives according to differential equations of higher order, typically to analytical dynamics of systems. Key words: analytical dynamics, mechanics, mass distribution, dynamics equations.