The multibody system transfer matrix method (MSTMM), a novel dynamics approach developed during the past three decades, has several advantages compared to conventional dynamics methods. Some of these advantages include avoiding global dynamics equations with a system inertia matrix, utilizing low‐order matrices independent of system degree of freedom, high computational speed, and simplicity of computer implementation. MSTMM has been widely used in computer modeling, simulations, and performance evaluation of approximately 150 different complex mechanical systems. In this paper, the following aspects regarding MSTMM are reviewed: basic theory, algorithms, simulation and design software, and applications. Future research directions and generalization to more applications in various fields of science, technology, and engineering are discussed.

The linear multibody system transfer matrix method (LMSTMM) provides a powerful tool for analyzing the vibration characteristics of a mechanical system. However, the original LMSTMM cannot resolve the eigenvalues of the systems with ideal hinges (i.e., revolute hinge, sliding hinge, spherical hinge, cylindrical hinge, etc.) or bodies under conservative forces due to the lack of the corresponding transfer matrices. This paper enables the LMSTMM to solve the eigenvalues of the planar multibody systems with ideal hinges or rigid bodies under conservative forces. For a rigid body, the transfer matrix can now consider coupling terms between forces and kinematic state perturbations. Also, conservative forces that contribute to the eigenvalues can be considered. Meanwhile, ideal hinges are introduced to LMSTMM, which enables the treatment of eigenvalues of general multibody systems using LMSTMM. Finally, the comparative analysis with ADAMS software and analytical solutions verifies the effectiveness of the proposed approach in this paper.

To study the dynamics of a vehicular missile system and determine initial disturbances of a missile, the multi-rigid-flexible launch dynamics model of a vehicular missile system is developed by using transfer matrix method for multibody system and launch dynamics theory. The overall transfer equation, overall transfer matrix, and characteristics equation of the system are deduced based on the automatic deduction theorem of overall transfer equation of multibody system. The equation governing the motion of the vehicular missile system is obtained by using the orthogonality of augmented eigenvector and body dynamics equations of the system. The launch dynamics equations of a missile are deduced, in which the mass misalignment and dynamic imbalance of the missile are considered. By combining the equation governing the motion of the system and launch dynamics equations of the missile, the launch dynamics equations of the vehicular missile system are developed. The vibration characteristics, dynamics response of the system, and initial disturbances of the missile are simulated. The simulation results show that the eigenfrequencies obtained by the proposed method and ordinary dynamics method have good agreement. Some factors that influence missile’s motion and initial disturbances are analyzed. The paper provides an effective approach to study the launch dynamics of a vehicular missile system.

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.