A Review on Dynamic Formulations in Multibody Systems: Mass Distribution, Higher – Order Acceleration Energies, Generalized Forces and Advanced Dynamics Equations

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Abstract
In multibody systems (MBS), such as robot structures, classical modeling is often based on simplified assumptions concerning mass geometry. This paper introduces a formal theoretical model to overcome these limitations by introducing the concept of mass dis-tribution, which describes the continuous nature of mass properties within kinetic as-semblies. Furthermore, the research integrates higher-order acceleration energies into the dynamic formulation – a topic less explored in conventional approaches. By applying the principles of analytical dynamics, particularly a generalized form of D'Alem-bert-Lagrange principle, a comprehensive model based on higher-order acceleration en-ergies is developed. Matrix exponentials and higher-order differential operators are ap-plied to determine the dynamic equations. Generalized forces are also analyzed as es-sential dynamical parameters, directly related to generalized variables and characterized by mass properties, including mass centers, inertial tensors, and pseudo-inertial tensors. The dynamic behavior of the system is described by using matrix-based expressions for defining kinetic and acceleration energies, and their time derivatives. The paper proposes a unified, matrix-based theoretical framework for modeling advanced dynamics in MBS, emphasizing the role of mass distribution and higher-order acceleration energies. This formulation facilitates a deeper understanding of inertial properties and dynamic inter-actions in complex mechanical systems such as robots.

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