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

TL;DR

This paper introduces an efficient formulation of Volterra's equations for multibody systems, reducing the number of equations needed and demonstrating improved performance through simulations of various systems.

Contribution

The paper presents a novel method that incorporates dynamical constraints from ignorable coordinates, streamlining the derivation of motion equations for constrained and unconstrained multibody systems.

Findings

The proposed method reduces the number of equations needed for system analysis.

Simulation results show improved computational efficiency over conventional methods.

The method successfully handles systems with holonomic and nonholonomic constraints.

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 dealt with 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.