Analytical Formulations in Lagrangian Dynamics: Theoretical Aspects and Applications to Interactions with Virtual and Physical Environments

Abstract

Multibody dynamics has its roots in analytical mechanics. Newton's second law directly implies that the dynamics of a particle along any direction of physical space is specified by either giving force or motion. This notion is extended under the Lagrangian approach to the general case where a system is considered as a generalized particle in configuration space. In this presentation, we elaborate on the principle of relaxation of constraints and some analytical aspects that give the possibility to establish novel representations for mechanical systems. A key aspect in our approach is the replacement of the direct consideration of constraints with a two‐step analysis, and moving the "force or motion" specification to the second step. This approach makes it possible to establish a more general view of multibody dynamics problems and address systematically non‐ideal and non‐perfect cases, as well as some groups of unilateral problems. Based on the proposed approach we will discuss different possible parameterizations of multibody dynamics, which can be advantageous for various applications (e.g., computational aspects, analysis, control). We will bring illustrative applications in analysis, design, and control from various fields of mechanical systems such as robotics, haptics and virtual environments, biomechanics, and vehicle systems.