Transfer Matrix Method for Multibody Systems

3Augmented Eigenvector and System Response

3.1 Introduction

By presenting the new concepts of the body dynamics equation of the body element and the body dynamics equations of a system in the transfer matrix method for multibody systems (MSTMM), the complicated global dynamics equation of a system is no longer needed in solving multiple rocket launch system dynamics (MRLSD). The body dynamics equations of a system are merely the assemblage of the body dynamics equations of the body elements of the system, which are totally different from the global dynamic equations of the system. It is also not necessary to consider the connection relations among body elements of the system because they have been considered in the overall transfer matrix and vibration characteristics of the system. There are uniform forms of body dynamics equations for various body elements, therefore there are very simple forms of body dynamics equations of systems for multi‐rigid‐flexible‐body systems (MRFSs). These make the writing and derivation of dynamics equations and solving the dynamics response more convenient.

The orthogonality of eigenvectors of MRFSs is the pre‐condition to calculate the dynamics response of the system accurately and makes the dynamics response quickly converge to the precision required by engineering in limited modals. For example, to assess scientifically and improve the performance of weapon systems, and to greatly reduce the consumption of ammunition in the test and realize ...