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

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.