Transfer Matrix Method for Multibody Systems

8Discrete Time Transfer Matrix Method for Multi‐flexible‐body Systems

8.1 Introduction

Generally speaking, for many engineering problems, a dynamics model of a multi‐rigid‐body system (MRS) cannot meet the demand of engineering accuracy. For example, to implement the dynamic design required for precision firing of artillery and rocket launchers, the gun barrel and the guider of the rocket launcher have to be treated as elastic bodies to meet the demands of engineering accuracy [1, 249]. Therefore, the dynamics models of artillery systems and rocket launchers have to be treated as multi‐rigid‐flexible‐body systems (MRFSs). MRFSs are systems composed of rigid and flexible bodies undergoing large motion connected by various hinges. In MRFSs, not only are the elasticity and damping of connection points, as well as the large motion of body elements, considered, but also the coupling of deformation and large motion of the elements. The MRFS is the refinement, natural extension and further development of the physical model of the MRS. Using ordinary methods of multibody system dynamics, the derivation of the global dynamic equations of the MRFS is rather more complicated than those of the MRS, and the computational scale and cost are also greater, while the theory of MRFS dynamics is not as perfect that of MRS dynamics. How to establish the dynamic equations of general MRFSs and improve computational speed is one of the primary research directions in MRFS dynamics.

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