Transfer Matrix Method for Multibody Systems

1Introduction

1.1 The Status of the Multibody System Dynamics Method

A multibody system (MS) is a system composed of many bodies, including rigid bodies, flexible bodies, lumped mass, etc., connected in various ways. The physical concept of an MS is ancient and unambiguous. In the construction of national defense and the economy, such as weaponry, shipping, aeronautics, astronautics, communications and mechanisms, many models of practice engineering, such as tanks, ships and warships, aircraft, carrier rockets, vehicles, robots, machine tools etc., can be regarded as MSs composed of rigid bodies, flexible bodies and lumped masses connected with various hinges [1–12].

In the 1950s to the 1960s, the concept of a multibody was either a multi‐rigid‐body or a multi‐flexible‐solid, therefore two totally different subjects, multi‐rigid‐body system dynamics (MRSD) [7, 9, 11] and the finite element method (FEM) [13], respectively, were developed almost independently. The infinite element method [14], presented in the mid‐1970s, perhaps is a little supplement for the FEM. The basis of MRSD is the ancient dynamics and variation principle. The research objects of multibody system dynamics (MSD) [6, 8, 12] are a rigid body and flexible solid, which includes both the research objects of MRSD and the FEM. Since the dynamics equation of a rigid body rotating around a fixed point was established by Euler in 1765, rigid body theory has had more than 200 years of history and is very distinct. ...