Transfer Matrix Method for Multibody Systems

4Transfer Matrix Method for Nonlinear and Multidimensional Multibody Systems

4.1 Introduction

Nowadays, nonlinear science is developing rapidly, bringing an unprecedented challenge to almost all disciplines and fields. Any physical system is nonlinear as long as it is analyzed precisely enough. Considering a real physical system as a linear system means that its main performance can be represented precisely enough by an approximate linear system. “Precisely enough” means the difference between the real system and an ideal linear system is so insignificant that it can be neglected for a particular matter. Whether to model a real physical system as linear or nonlinear depends on the specified requirements and conditions.

Essentially, the transfer matrix method for multibody systems (MSTMM) transforms the problems of developing the differential dynamics equation and its solution into problems of developing the transfer equation describing the relation between the state vectors of input and output ends and its solution. The transfer direction is unidirectional and one‐dimensional for the classical transfer matrix method (TMM). The methods for dealing with the tree system, closed‐loop system and framework system, which are common in engineering, are studied in Chapter 11. These are also one‐dimensional methods.

In this chapter, the strategies to solve the dynamics of nonlinear multibody systems by using the MSTMM are introduced. The following topics are included: solving the steady‐state ...