Development of an Efficient Formulation for Volterra’s Equations of Motion for Multibody Dynamical Systems

Yoosefian Nooshabadi, Mohammad Hussein; Nejat Pishkenari, Hossein

doi:10.24200/sci.2024.60600.6891

Development of an Efficient Formulation for Volterra’s Equations of Motion for Multibody Dynamical Systems

Document Type : Article

Authors

Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

10.24200/sci.2024.60600.6891

Abstract

In this paper, we present an efficient form of Volterra’s equations of motion for both unconstrained and constrained multibody dynamical systems that include ignorable coordinates. The proposed method is applicable for systems with both holonomic and nonholonomic constraints. Firstly, based on the definition of ignorable coordinates, one of the motion constants (the generalized momentum vector corresponding to the ignorable coordinates) is considered as a constraint, which will be referred to as dynamical constraints. These constraints, along with ordinary constraints, namely kinematical constraints, are then used in the proposed method to derive motion equations. This approach gives the minimum number of equations needed to study the behavior of a dynamical system. Three simulation examples are provided to evaluate the proposed method and to compare it to existing methods. The first case study is a constrained dynamical system, which moves in two-dimensional space. The second one is an unconstrained multibody system including three connected rigid bodies. Finally, the last case study includes a cubic satellite that uses a deployable boom to move a mass to a desired location. The results of the numerical simulations are compared to the conventional methods and the better performance of the proposed method is demonstrated.

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