Solution of constrained mechanical multibody systems using Adomian decomposition method

TL;DR

This paper introduces a direct Adomian decomposition method for efficiently solving the complex Euler-Lagrange equations in constrained multibody systems without complex transformations or index reductions.

Contribution

It presents a novel application of the Adomian decomposition method to index-three DAEs in multibody systems, simplifying the solution process.

Findings

Efficient solution without index-reduction

Applicable to robotic system equations

Requires only solving linear algebraic systems

Abstract

Constrained mechanical multibody systems arise in many important applications like robotics, vehicle and machinery dynamics and biomechanics of locomotion of humans. These systems are described by the Euler-Lagrange equations which are index-three differential-algebraic equations(DAEs) and hence difficult to treat numerically. The purpose of this paper is to propose a novel technique to solve the Euler-Lagrange equations efficiently. This technique applies the Adomian decomposition method (ADM) directly to these equations. The great advantage of our technique is that it neither applies complex transformations to the equations nor uses index-reductions to obtain the solution. Furthermore, it requires solving only linear algebraic systems with a constant nonsingular coefficient matrix at each iteration. The technique developed leads to a simple general algorithm that can be programmed in Maple or Mathematica to simulate real application problems. To illustrate the effectiveness of the proposed technique and its advantages, we apply it to solve an example of the Euler- Lagrange equations that describes a two-link planar robotic system.