Transfer matrix method for multibody System (MSTMM) is a new multibody dynamics method developed in recent 20 years. It has been widely used in both science research and engineering for its special features as follows: without global dynamics equations of the system, high programming, low order of system matrix, and high computational speed. Based on MSTMM and its above features, a theorem to deduce automatically the overall transfer equations of multibody systems by handwriting or by computer is proposed in this paper. The theorem is effective for multibody systems with various topological structures, including chain systems, closed-loop systems, tree systems, general systems composed of one tree subsystem, and some closed-loop subsystems. This theorem makes it possible to program large scale software of multibody system dynamics with much higher programming, and much higher computational speed because of the above features of MSTMM. Formulations of the proposed method as well as two examples are given to verify this method.

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Compared to classical mechanics, the transfer matrix method for multibody systems is a rather novel approach for analyzing multibody system dynamics. For its features that it avoids the global dynamics equation of the system, keeps a high computational speed and allows highly formalized programming, this method has been widely used in science research as well as design of dynamics performance and experiments for various complicated mechanical systems. Up to now, there have been more than 50 research directions in science research and key engineering applications based on this method. In this paper, the following aspects are systematically reviewed: history, basic principles, formulas, algorithm, automatic deduction theorem of overall transfer equation, visualized simulation and design software, comparison with other dynamics methods, tendency, and future research directions.

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The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain multibody systems with the transfer matrix method for multibody systems (MSTMM). However, for linear tree multibody systems, the recursive relations of the Riccati transfer matrices, especially those for elements with multiple input ends, have not been established yet. Thus, an RTMM formulism for general linear tree multibody systems is formulated based on the transformation of transfer equations and geometrical equations of such elements. The steady-state response under harmonic excitation of a linear tree multibody system is taken as an example and obtained by the proposed method. Comparison with the finite-element method (FEM) validates the proposed method and a numerical example demonstrates that the proposed method has a better numerical stability than the normal MSTMM.

The purpose of this paper is to present a comprehensive multibody system dynamics model of a multiple launch rocket system (MLRS), and implement its simulation and experimental studies. The new version of transfer matrix method of multibody system and the launch dynamics theory are used in deriving the equations of motion coupled with rockets and barrels. The obtained model accounts for the complete process of the rockets’ ignition, movement in the barrels, airborne flight and landing. Launch dynamics of an 18-tube 122mm MLRS is investigated in this paper. Considering the effects of random factors, such as the impact and clearance between the rockets and barrels, the mass eccentricity and dynamic unbalance of the rockets and the thrust misalignment in this model, and combining the Monte Carlo method, the simulation of the dynamics of MLRS is carried out. Finally, the experimental implementation is proposed and the experimental results emphasize the feasibility of the multibody system launch dynamics model as a viable alternative for modeling accurately the dynamics characteristics of a practical MLRS. Meanwhile, the correctness of the numerical results is validated.